Well, if we're sticking with her missing both arms, there are still ways to get around this. She could use prosthetics. They aren't good for fine motor controls, but she could figure out a way to use them to draw cards I'm sure. Also, she could simply ask you for help. A big part in raising her will be teaching her that it's okay for her to ask for help sometimes. Like I said before, young girls can be very stubborn or independant, which won't really be something she can be all the time. By learning when and how to ask for help, she can become more confident in the future if she ever needs help, yet is concerned about feeling like a burden. There are times when she simply won't be able to do something, and that's okay. In this case, you could draw a card and not look at it, and simply set it where she's keeping her other cards. It's also a trust building exercise in a way, because it teaches her that not only can she ask for help, but that help will be genuine and not a bother to the person providing it.
As far as moving figures (again, I don't play tabletop games so I'm not sure what the motions are exactly), the same holds true. Prosthetics are an option (and it's best to get her used to them as early as you can, so she can grow up with them more). Hell, before we know it there might be real robotic limbs, she might one day have more grip strength than you! Being patient with her and including her in things she thinks that she won't be able to do will help her confidence in many ways. It also shows that no matter what, being disabled isn't nearly as much of a handicap as is often portrayed in books or movies. She can live a normal life, she just needs a little help sometimes.