I'm Brazilian and learned English mostly through gaming, too. That, and the basics I got at school plus watching loads of Youtube later on.

I don't really have this same urge as you do, but personally I used to think my speaking was quite bad (because it's the one skill I never use), but then there was this one random day where I played Splatoon 2 online with some dudes from here and after a few minutes it was totally natural.