I think I'd learn towards minimizing the 'gamer' aspect. Nothin' wrong with coding and web development.
So, something more like this:
--> When I was a child, my father was a web-developer. I was always interested in his work, but at the time, didn't pursue it further.
--> Throughout high school, I competed very seriously in different online gaming communities and my team was highly successful.
--> Wanted a website for an online gaming team I was involved with (just mention gaming in passing), but realized that the available options were not sufficient for what I was looking for.
--> So, I decided to self-teach myself how to design and code dynamic, php driven websites.
--> After several ups and downs, I now operate a successful website development business with several customers,
specifically oriented towards competitive gaming teams..
You can illustrate that you can learn on your own, you're self-motivated, you can turn a personal interest into something 'real,' and all sorts of good stuff that adcomms would like, without focusing too much on the aspects that would make the reader think of the gamer living in his parents' basement eating chee-tos.
