A game with such a bleak, grim, and soul-sucking premise has no right to be so addictive and replayable. It has a strong narrative (with 20 different endings), meaningful social commentary, and some of the best moral choices I've seen, that can really wear you down and make you uncomfortable. It will pull you in and refuse to let go, and it's one of the most unusual games you'll ever play.
Papers Please isn't "fun" in the traditional sense though. Checking passports and documents for discrepancies is inherently tedious. There's some satisfaction to be drawn from getting faster and more effective at the job, and from spotting small things that are easy to miss, but a lot of the time it really does feel like work. Most of my enjoyment in the game didn't come from the mechanics directly, but from how the mechanics effected the world, story, and the characters within it. But this isn't criticism at all. Actually, this is praise. It puts you in the shoes of someone whose position you wouldn't want to be in, and uses that to full effect in order to enhance the atmosphere.
Papers Please taught me a valuable lesson. Games don't have to be "fun" to be good games, but they must be engaging, and they must allow me to have meaningful interactions with the world. This game isn't really fun, but it's very engaging and incredibly interactive. I love it. It's not for everyone though.