You're not teaching her to "play xbox", you're teaching her to play a certain game on the xbox. Either get a new game (as suggested) so you both learn together, although I think previous experience in gaming means you'll learn about 200x quicker than her which could cause some frustrations or play a game that she says she thinks is interesting. There's not really a way to teach people how to play games, they need to work it out for themselves (of course guidance helps).
I had a little local game of TTD over xmas between, me, my brothers, my little sister and the oldest brothers GF. Only me and my brothers had played before, and we had a lot of experience in it (childhood game = played too much). My little sister was 12 at the time, playing on a crappy laptop (kind of unfair, oh well), we were constantly getting asked how to do this or that (we'd explained the overall objective, which is important to do I'd guess).
Back on point

Let her work out what she needs to do to get to the objective, where it kill everything infront of her, or just get around the corners without crashing (racing isn't really a hard objective to work out), and give information on how to achieve that (shoot from cover, drive a bit slower etc etc) and let them feel they've achieved the end result rather than you told them how to do everything. Remember, the end result is for her to enjoy the experience.
If she doesn't think games are worth her time, it might be a bit harder obviously

If she doesn't want to play games, there is no point forcing her, but if she gets interested in a game you're playing, just offer her the chance to play. pc has benefits in the area, you can "share" the control so they don't feel as useless at the game to begin with.
Also, everyone hates to lose, but people will never start at the top, in anything.
Note: I've been writing lots of long posts full of waffle today, try and find some information somewhere in what I said
