Ah, Yu-Gi-Oh. I had fallen for the card trading fad back when this anime caught on, and thus, I played some of the GBA games from the 2000s. This was the second one I remember playing, and thus, for nostalgia, I went back to see what was up with Eternal Duelist Soul.
It sure captures what the card game was supposed to be, and there's a LOT to take in. For anyone that never played, don't go into this with the expectation of this being a simple kids' game. It's a deep system.
Prior to each duel, the game makes you play rock, paper, scissors to determine who will go first. You or the AI?
Both players start with 5 cards. When it's your turn, you draw a card from your deck. You can summon a monster with 4 star ratings or less, per turn. Monster cards can have no additional effect (Yellow), or they can have effects (Orange). Trap cards (Pink) and Magic cards (Green) can be set and activated with no real limits, other than their particular effects.

When it comes to monsters with effects, they can involve flipping the card over from face-down position (Big Eye, for example), or they can be continuous (like Jinzo, one of the better cards in the whole game).
Monsters with 5 and 6 star ratings will require the sacrifice of a monster that's already on the field. Monsters with 7 or 8 require two sacrifices.
If you have more than 6 cards in your hand by the end of a turn, you must send one to the graveyard. Monsters in the graveyard can be brought into the field with magic/trap cards like Call of the Haunted or Monster Reborn. If a monster is "removed from play" due to an effect, tough break, those previously mentioned card won't work on that monster.
There are also monsters that can be fused via the magic card known as Polymerization, and there are also Ritual Monsters that can be summoned by Ritual magic cards, and...
It's better if I just stop with the details here - the point is that this game got the rules just right. To win, you have to reduce your opponent's life points to 0. This can be done via attacking your opponent when there are no monsters on the field defending said opponent, or whenever you attack a monster that is weaker than yours. You can also engage in troll tactics that lead to them losing cards. If a player has 0 cards left, and is in a situation where they must draw a card, that player loses.
This is the kind of game that is easier to learn as you go along, rather than having me dump a load of text about all the intricacies of it.
You may have heard of Pot of Greed and its ban, but forget about that. The card was perfectly legal in this game. Ditto for Cyber-Stein.
When you start a new game, you will be greeted by Tea Gardner, a friend of the titular character, Yugi. You have to choose your deck, and I always go for the black deck, personally, since it emphasizes monsters. The others are self-explanatory: middle emphasizes trap cards more, right emphasizes magic cards.

After a bit more chatter, you should go check what's in the deck you chose. The main menu of the game is this:

From experience, I mostly spent time in Campaign and Deck Edit. "Record" is a completely useless option that shows your win-loss-draw record against characters, something you already see in the Campaign menu. If you're playing alone, Link Battle and Card Trading are useless options. Calendar is something you should check every now and then, because after a duel in the Campaign option, a day will pass. Special events can take place on different days. Password has a very neat idea that I still find to be a masterpiece of marketing.

So, the actual cards have a number on them. For example, Gemini Elf is a card that some tougher AI opponents like to use in this game. In real life, the card itself has a number: 69140098. If you put that number in the Password system, congrats, you now have Gemini Elf. Why is this useful? It has 1900 attack points, and requires 0 sacrifices to summon. Very useful to have against the early opponents in the game.
Early opponents? Well, this is where things start to decay a bit.
(Side note: the Password has its limits. For instance, you can't just get Gemini Elf 40 times to fill your deck with it. You have a limit of one use for each Password. Some cards in general have a limit of 2 and 1 per deck.)
When you go into the Campaign menu, you will only see the first tier of opponents. Get used to them, because you have to defeat each of them twice to unlock the second tier. That's not too bad since these are easy opponents, right? Well, duels aren't exactly short ordeals...and the duels get tougher later on.

The soundtrack captures the friendly vibe of these characters just fine with the music that plays during the intro and the duels themselves. If you saw the anime, you may even feel yourself sucked into the world of the anime, having a comfy game with Yugi and his friends at school.
Let's say you unlock the second tier. You'll have to press R to see the tier, and you'll find 5 new opponents.

They are a little more difficult to deal with, and to unlock the third tier, you have to beat these characters 3 times. Yes, three wins over each character. That's 15 duels, at least. Even if you're an ace, you're going to get bored after a while. When you beat an opponent, you get the outro of the character you beat, and then you pick a booster pack, which will contain 5 cards - at the beginning, most of the cards you can win are, frankly, poor. You can unlock more useful booster packs as you unlock tiers, but the really useful booster packs have ridiculous requirements.
For example, there's a booster pack with the image of a Gemini Elf card. To unlock that, you must defeat Mako Tsunami 20 times. 20 TIMES! Defeating Mai Valentine 20 times unlocks a Launcher Spider booster pack, which seems like a mistake. Shouldn't you get that if you defeat Weevil (kid with the glasses), since his theme is bug monsters? In the first tier, the requirements are like this as well. Defeating Yugi 20 times unlocks the Blue-Eyes White Dragon booster pack. Shouldn't that have been saved for defeating Seto Kaiba X amount of times? That dragon is his signature monster card. There is an Exodia booster pack, but you get that after defeating Joey 20 times.
Since I don't play modern Yu-Gi-Oh games, this just makes me wonder how predatory these games can get. Imagine, if instead of having to duel so many times, the game offers unlocking those booster packs with a low price of 5 dollars in real money...how gross!
For those that don't know what a Seto Kaiba is, he's a major character in the Yu-Gi-Oh anime that was airing at the time this game came out. He is a fourth tier character. We didn't even touch the third tier, so let's look at that first.

This is where the duels can get annoying. Rare Hunter (highlighted in the screenshot) has an Exodia themed deck. He will try to get the 5 cards that represent Exodia's body (head, left arm, right leg, etc.) - if he succeeds, he wins the duel automatically. Barring the effects of a magic card like The Forceful Sentry, you can't see the opponent's cards in his hand, so...this guy is a real prick to deal with. Others will have bothersome trap cards like Trap Hole, Mirror Force, etc. - I'm used to dealing with jerks like these, but rookie players will have to go through trial and error.
Thing is, the trial and error involves lengthy duels, so that can be off-putting. Granted, these days, there are guides that tell you exactly what cards each jerk in this tier has. The luck of the draw can still work against you, though. Keep in mind, you have to have at least 40 cards in your deck. The side deck (limit of 15 cards) comes in handy during special duels where your Campaign is interrupted by a little scene telling you that some weekly gimmick is going on. This is why it helps to check the Calendar option every now and then. Those special duels are in a best 2-out-of-3 setting. Between each duel, you can swap cards between your main deck and your side deck.
Now, even as a grizzled veteran of this game, Umbra & Lumis (far left) gave me some laborious duels where I only won because I forced them to lose cards, to the point where they had 0 left, making me win by default. There's an art to getting good at this, but it takes time, and if you're not already familiar with what a Yu-Gi-Oh is, then you probably won't want to put in that time.
Speaking of time, let's say you went through the grind and unlocked the fourth tier.

There is a fifth tier after this, which is the final one, but you know the pattern. You have to defeat the opponents here (current tier + 1) times to unlock the next one. In this case, that means 5 wins over each duelist. 25 duels at the very least.
In general, making progress in this game is a chore. That's the biggest issue by far. For a smoother, less laborious experience, play Yu-Gi-Oh! Worldwide Edition: Stairway to the Destined Duel.
Additionally, I must mention that there are glitches in this game, but through normal gameplay (i.e. not playing in a way that's looking for glitches), I only came across one with Giant Trunade and Call of the Haunted. I will mention some to close out the review. Credit to the Yu-Gi-Oh fandom site for these:
If you use Change of Heart more than once in the same turn (for example, by using it once, flipping Magician of Faith and returning it to your hand, and then using it again), only the last card you use Change of Heart on will return to your opponent's field at the end of your turn. The other(s) will remain under your control.
Once you play Graverobber, set the card instead of immediately activating it. Once the card is set, activate it and you will not lose 2000 Life Points.
The CPU plays Spell Cards even when Imperial Order, which negates the effects of Spell Cards, is face-up on the field.
Giant Trunade is a useful card, but also has multiple glitches:
If you used Call of the Haunted to revive a monster, you can use Giant Trunade and the monster will stay in the field.
If you used Snatch Steal to take control of an opponent's monster, then you can use Giant Trunade to return Snatch Steal and you keep the opponent's monster.
You can not activate Tribute to The Doomed if the card is set and you have no cards in your hand to discard, however, you can play Tribute to The Doomed without discarding a card when that card is the only card in your hand.