My son is four and while we don't have any games for him to play on the computer nor a gaming console I know that when we go to the public library he loves to sit and play the educational games while we are there. He can't always do it by himself, but I sit and try to help him when he needs it. I also know that at his preschool they have a game on the computer that he enjoys playing when it is an option.
He by no means asks to go to the library to play games, but he does recognixe when I or my husband is playing a game on the computer (solitaire or sudoku) and asks if he can help or watch and we hold his hand on the mouse and he helps.
So, with all that said, I think that if you daughter is interested that might be something fun for her to do occasionally. I don't think she'll ask for it everyday but it may be more frequently at the beginning (like any new toy) and then start to lose it's appeal. I would just be careful of being clear on whatever computer rules you have. Our son is four, he knows the computer is not a toy and that he is not to touch it unless mommy or daddy is helping him. We have to be clear because we also have a two year old, and so the rules are the same for both. If my son ever were to ask about using the computer I would probably tell him that he needed to wait until his sister was napping because she isn't allowed to use the computer, just like if he wants to paint. He understands and tries to be patient but usually tells me that she is tired and ready for her nap right then. :)
Just make a game plan with your husband and see how it goes, you can always change it - that is the beauty of being a parent. :)
One more bit, I don't know what type of game that is, but be careful of competition. I have a nephew who is 5 and plays the Wii with his brothers and sisters and is quite good at some of the sports things. Well, he and my son played over the holidays and my sister had to turn it off because he started saying mean things to my son (who had never played before) like "Ha Ha you're gonna lose!" "Watch me, I'm better". Now, I'm not one of those people who thinks everyone has to be winners and their can't be any loser, but son didn't care about what he said, but the tone he said it in was very mocking and rude. So, just something else to watch for.
Good Luck!