Is it a horror game? Definitely not. Although it's very drab with lots of nasty choices to make... And ultimately your morals will be tested. Should you do your job correctly to the letter, even if you know in your heart that it's not always the 'right' thing? Or are you gonna switch off your emotions entirely and just be a part of the machine? The choice is yours. But be prepared for reprimand if you choose the former. The game is excellent and addictive.
Papers Please is a 2D game by Lucas Pope, who has previously worked on UI and Tools stuff for Naughty Dog, most notably for games like Uncharted. At some stage he decided to leave that comfortable job and start off on his own. He was inspired by Passport Control officers and figured it would make a cool game idea. Strangely, he was right (he's also made another game called Return of the Obra Dinn since, and that too is excellent). Papers Please was released on PC and Mac first, then made its way to Linux, PS4, Vita and iPad.
So what is the game? You've just been selected to work on a new border checkpoint to your home country of Arstotska. The game has distinct Soviet-era style and tone (but it is never suggested that it is Soviet and does a good job to distance itself from those kinds of terms. For example, you'll never see the word "comrade" in the game) and it's your job to run the checkpoint, calling the next person, asking for their documents, checking if everything is in order and then either allow them to enter or deny them and send them back. Ideally you want to get as many people at your window as possible for maximum pay, as the government pays per person on top of your basic salary.
If you get things wrong, you get a citation. Get too many of these and they will start to deduct pay. Then later your superior comes to visit and will give you a kicking. If performance stays poor (or gets worse) you lose your job and everything else. On the flipside, if you're consistently good you will be told that you are working satisfactorily and then they'll give you a plaque to put on your wall (also, you HAVE to put these up or again you will get reprimanded).
As the game progresses, there's extra complexity that gets thrown in such as needing more documents and other things to verify and confirm. The game shakes things up often enough and it's always a real race against the clock to accurately move these people around.
In a normal game, you have access to a handbook which tells you what you need to be looking for in terms of documentation, as well as a map with all of the countries in the area and their issuing cities. On a persons passport it will generally have a passport photo, passport number, issuing city, date of birth and expiry date. All of these need to be checked for validity and you also have to cross-reference them with other documentation they provide. You can speak to people for more information and also confront them on any issues if needed.
The game doesn't just let you do this at will though, you can only interact with people if you have a valid reason to. Which is where the Inspection Mode comes on. Here, you toggle a mode where you select an item you think is invalid against something else (e.g. If you think their issuing city is wrong, you would select the issuing city on the passport against the list of issuing cities in your handbook, or if their photo doesn't look like them, you'd select the photo along with the person in the booth). From there you can either deny them or (at least later in the game) detain them.
There's extra complexity added later that simply has to be experienced (there is an entire sub-plot involving anti-government factions and you can also have access to guns as well), I would rather people play the game than explain every little gameplay element; all I can say is that it's a surprisingly thrilling experience and I've been playing it for years on-and-off.
The main game has an overall plotline, that mainly exists to try and throw some spanners in your works. There are a bunch of scripted encounters that always happen, for story reasons and there are also randomly generated people that get thrown into the mix. Essentially the game forces you to make choices that can and will eventually harm you and your family. On that note, there is also a simple post-level mechanic where you have to decide how to spend your salary on yourself and your family. Basic stuff like food, heat, medicine etc. It's possible for family members to die if you don't perform that well at work which will affect the game ending (and there are multiple endings).
So yeah, I hope this review has at least piqued your interest in Papers Please. It's a devilishly simple game with a dull-sounding premise. But it's great.
Also, there is an Endless Mode that you can unlock if you beat the games 'main' ending. And the iPad version is probably one of the best games for the platform as you have full touchscreen controls. It's not available on iPhone as the screen area is too small.