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I used to be an avid fan of computer games and I was a gamer at my childhood. Now, I do not get enough time for such things and on top of that I am mature enough that I do not like to play childish games.
Comments  
"I used to be an avid fan of computer games, and I was a gamer as a child. Now I do not have time for such things, and on top of that I am mature enough that I do not like to play childish games." Two independent clauses connected with a conjunction like "and" are separated with a comma. "At my childhood" is not indiomatic. "In my childhood" sort of works, but it sounds odd when you have "as a child" or even "in childhood". No comma after "now" because the comma makes it the introductory "now", which has a different meaning than the one you want, which is "these days". "Get" is not wrong there, but you mean "have". "Enough" is unnecessary and sounds it because "I do not have time for" already means that. That pesky comma again.