You always need to consider which niche you want to target. For example, if you make Minecraft or Fortnite videos, you probably should do something much more specific, since there are already SO MANY videos. Consider something like "Minecraft 15.2 (or whatever the latest version is) co-op lets play" or "Fornite no building challenge". I don't know if those would work, but I hope you get the point.
Your content doesn't have to be necessarily something like that, but if do your SEO you should aim for niches within the game you are playing.
And if you make many videos of the same game, YouTube learns that your channel is a lot about that game and gives you a boost in the search results. This is channel authority. Also, if you focus on one game, people who are interested in that content are likely to watch other videos of yours about the game. So you might want to consider focusing on one game. Just take a look at successful gaming YouTubers and you'll see that most started focusing on one game.
But besides that, it doesn't really matter. The thing is with popular games like Minecraft, your only chance to compete is to go with very niche terms, which of course give you not that much traffic, but still more than nothing. If you play less popular games, you can go with less niche keywords for them, but those games also get less traffic overall. So it pretty much balances itself.
Just play some games and see what you like playing the most and what your audience likes.