I might be against the majority on this, but I would say put it in. It seems it had a huge impact on you and made the person you are today.
I would not focus on the gaming part of it, but rather the impact it had on you, and what makes you want to play this until now.
I had something similar (for a different language since I grew up abroad as a 3rd culture kid), and included it. I focused on the language exchange part of it, and meeting others through it. I found some long-term friends through it who I am in touch even until now without never having met them in-person, and helped each other learn our languages.
Although no interviewer of mine commented on it (even those who had my application in front of them), but it seriously had an impact on me, and I would attribute the extroverted and confident side of my personality to this as I used to be an extremely shy kid and teenager when I did not fluently speak the language of the majority.