Go for the date.
I've played many games on a competitive level (SSBM, SSBB, Pokemon RSE, Pokemon DP, Call of Duty), and I've won quite a few tournaments for each of them. And you know what? It's very very satisfying, winning a tournament. It feels great when you realize that all that hard work you put into a game-- refining your skills and studying the latest strategies-- has finally paid off.
But you also know what's even better? Being with someone that you like. There's something about romantic companionship and love and all of that stuff that can't be fulfilled by playing a video game in a tournament.
I am pretty obsessed with video games in general. I've been playing them since I was 3. I own 7 systems, and have over 180+ games. I'd say I'm addicted. There were times where I spent on average 16 hours a day playing games (summertime). And even the games that I don't play on a competitive level, I still try to master and I still try to complete every possible task within the game. Why? It gives me pleasure and satisfaction, knowing that I can put hard work into a game and achieve the final end (unlocking everything, mastering the game, beating everyone else in it, etc etc).
But as much as I love video games, I would give it all up to be able to experience everlasting true love. Video games are fun, yeah, but when you love someone and they reciprocate those feelings, that's basically a life-long friend and partner that you have. It's much more important than the temporary pleasures you might get from a game.
I mean, it's probably not the case that if you tell him you're busy, that he'll lose interest in you forever. That's probably not going to happen. But even so, think about it. What the two of you could potentially have is something that not every can achieve, at least not easily. There are tournaments all over the place. They happen often, and you'll have many chances to win money in them. But it isn't often that you like someone and they like you back.