Harry didn't play DnD or MtG though. He lived in a magical world, and while some of those magical things occasionally caught his attention, he wasn't really deeply interested in any of it. His main concerns were social: casting unsubstantiated aspersions on Snape and Malfoy and occasionally being correct. He didn't care about any of his classes. His only real love was Quidditch, which he was naturally talented at, making him, if anything, a jock.
Rethinking through the series, which I have re-read within the past year, the only truly nerdy moments he has all involve girls; and then only really at the beginning of his involvement with girls. Very quickly, he begins to have quite mature thoughts regarding his relationships, even if he doesn't always make the right choices.