I was looking to openly discuss what other people use for the criteria of acceptable and unacceptable games and why they use that.
It's a good question to apply to anything we do.
I am not claiming to perfectly follow my own standards in everything I do in life. Just saying I'm not setting myself up as "Holy". I can see a godly reason for planting a flower garden, but some of my artistic stuff is strictly for its own sake.
But the most reliable guide for such a question, IMO, is to examine how it affects our relationship with God.
Does it do anything to move us further away from God? Then we shouldn't do it. (Some video games should certainly fall in this category according to anyone's discernment.)
Does it move us closer to God, or even to each other in true brotherly fashion? Then it has value.
The level of discernment and watchfulness we have over our hearts and minds will determine how easily we can make these choices. If we are not very experienced in watchfulness, we may not be able to answer that question for a wider range of options. But with practice we can improve.
And honestly, the way our spirit works will determine how we interact with things. For those who are more purified, they are less likely to interact with activities in an impure manner. But at the same time, they are more sensitive to lesser impurities.
That's the theoretical and thought process for me.
How that works out for me? I will play card games when I get together with people, because it's a way to interact. I'd be just as willing to play Pictionary or a board game we treated as fun for everyone (I'm sure there are exceptions I wouldn't condone for myself). If people get competitive and resentful, I wouldn't want to do it. But we laugh and enjoy and joke.
I am a gamer from way back. I don't personally play first person shooter because the thought (and image) of killing people makes me nauseated. I'll play fantasy games of killing monsters or robots because it's just fantasy and they aren't people. And some of the games I play use names of false "gods" for some of the entities in the game. I don't worry about that because I don't believe in any of it anyway. If it involved recreating any rituals, I wouldn't play them.
I've played paintball years ago. I wasn't concerning myself with morality back then, but looking back there was no malice or resentment, only fun. In the right mindset it's ok I would think.
Sports are mostly for exercise - if the competitive aspect becomes damaging between persons it's not edifying, I would say, but as fun and exercise it can be healthy, IMO.
But those interpretations will vary with persons. Someone who is very sensitive to certain things with a weak conscience (like the idol names used in games) shouldn't play them - much like St. Paul said that food sacrificed to idols was nothing, but due to weaker consciences of some, those brethren needed to be respected for their own conscience's sake.