I play games on Facebook occasionally and I can tell you that at some point, most people (including gamers) get annoyed by the constant game requests popping up everywhere, even your phone! You don't have to be a victim to these requests and you don't have to unfriend the people that are sending the requests. You can take control of the issue.
Some things to think about:
1. Don't blame the gamers. They aren't bugging non-gamers on purpose. Seriously, they don't get some secret thrill from getting on your nerves with their requests. Blame the games if you need to find fault somewhere. It's basic business marketing schemes at work in cyberspace. If a gamer sends you a request, then they assume that you play or it was an accident.
2. Gamers aren't sending you requests every day. Well, not always. If your name is somehow in the list of people who play the game, most gamers aren't checking through the names of request recipients so you're getting it accidentally along with the real gamers. Invitations to games might be made once then the game will send the request to you every freaking day in the hopes that you will finally be bored enough to check it out one day.
3. Don't be mean and rude to gamers because you're irritated by their games. People that do this make me really mad because it tells me that they don't care about the person they're calling out. It also tells me that they are too lazy or incompetent to figure out a solution to the problem without resorting to such low actions. You have the power to fix the problem. If you don't know how, then I assume you at least know how to Google it and find the solution. Right? It's not difficult and if you care enough, you'll find the time. It's no different than people using coupons and price-matching at the store or the old person wearing out their brakes while driving 5 mph with a line of cars behind them. If you can't bring yourself to do anything because you feel the gamer should take control of the situation, then at least send them a private message. Don't embarrass them. Not cool.
4. Don't assume that gamers are lazy slobs with no life. Many are introverts and it's their way to escape or relax. It's no better or worse than watching tv or reading a book for relaxation; it's just different. Many people also have jobs or situations where they spend a lot of time waiting for other people. That gets boring! All I'm saying is instead of being critical and judgmental, you can try being understanding.
5. You will not offend a gamer by blocking a game or ignoring a request. No one can play all of the games out there and everyone does this. Gamers understand that it's not everyone's cup of tea. In fact, the gamer will be relieved to know that they are not going to accidentally annoy you with their games if you chose to block the games.
6. How to block. It's a pain but once blocked, it's done. Until Facebook pulls one of it's usual stunts. When you seen the game request, type in the name of the game and go to their Facebook page. NOT THE APP! To the left of the game's page, you will see three dots next to "Share". Click the dots and scroll down to "Block Application".
You can also click on "Games" on your newsfeed page (left side under "Apps"). At the top, click on "Activity". Then you can choose "Invitations" or "Requests". Click on the game name. A box will come up inviting you to Play or Cancel. Look at the bottom right of the box. Click "View in App Center". At the right you'll see some options including the Block option. Click it and you're done.
I hope you find this helpful and that it will help create peace and understanding on this topic. We fight about enough things, lets cross this one off the list. It's easily remedied. I hope you care enough about your friends to try.