I went to my wife for this, and here is what she had to say.

Advice for you:
Definitely make it a priority to talk about this with your significant other. Not only could this issue be a problem in the future, and therefore needs to be discussed...but not talking about important issues (such as this) is in and of itself a bad precedent to set. Communication is the most important thing for a long term relationship. Set a time and place, and talk about it.
Don't ever let gaming become more important than your relationship. That doesn't mean she has a right to make you give it up, but if it dominates all facets of your life and relationship, then it's become a problem. When it comes right down to it, friction in a relationship over gaming, is really no different then friction in a relationship over football, golf, etc. Keep it as part of your life, but keep it as
part of your life...not your whole life.

Advice for Her:
If you're in Love with this guy, and want to spend your life with him, you have to accept him for who he is...warts and all! You can't change him to make him the person you wanted. If he's already not the person you wanted,
then he's not the person you want! But, as with any guy, there are always going to be things they like to do that you may not enjoy doing yourself - and vice versa. And that's okay. That's life and relationships. If his hobby becomes more important than you, then there's a problem (but that doesn't mean you can go testing his loyalty to you with a
"it's me or gaming" ultimatum...).
I'd suggest at least trying it out. If you don't like it, that's okay. But if it's something that you end up seeing as no big deal, game with him. You don't have to get into it nearly as deeply or intensely as he does, but doing something with him that isn't necessrily your cup of tea, shows you love him and engenders trust. But that also goes just as strongly for things that you like and he doesn't, and that you want him to be a part of (if even in just a limited way).
Sure, gaming is, to a certain extent, an immature hobby...but so is Golf, Football, fishing, etc. - and just as equally bookclub, scrapbooking, recreational shopping, and so on. Men and women both have hobbies, and no hobby is inherently less mature than any other. You both need avenues and interests outside of the relationship. As time goes on you'll find them necessary...and that's completely normal. But when any of those interests begin to dominate or overshadow other aspects of the relationship, especially when it's
"together" time, then things need to change. Those interests either need to be dialed back (preferred), or eliminated if necessary...but only if necessary. But as much as a hobby dominating a relationship can be devastating to it, denegrating something that is very important to someone in the relationship can be just as devastating. If you call his interests
"immature", you're also calling him immature. No different than if he called your interests
"silly". Good natured ribbing is always okay, and hopefully exists in your relationship (it's a sign of trust and intimacy), but scorn (even percieved scorn) can be fatal.

Above all though, you must talk about this. Communication is everything.