This is the "willpower" theory by Baumeister. There's a book of the same name.

The theory is controversial. The effect likely isn't too big, or it would be harder to design experiments where it doesn't show up at all.

But even assuming the theory is correct, playing video games wouldn't be considered beneficial, at least as long as you are enjoying it.

This should be somewhat obvious: if you enjoy doing something you are obviously not training your capability to do something that you don't enjoy.

The closest you can get to have license to indulge is that Baumeister would predict not playing video games (when you would like to do so) will deplete your willpower, and make it harder to resist other urges (such as not working) for that day. Over the longer term (several weeks) however, repeatedly resisting that urge to play would train your willpower.