Although young children don't improve their fitness levels in the same way adults do when they "work out" or exercise, it's not harmful to do some physical activity that mimics the type of movements that are involved in skiing.

We're putting kids in sports at a very young age, sometimes as young as 3 for soccer and basketball leagues. The whole purpose of these leagues is to get kids ready to play the "real" game. But that results in getting them ready to play games rather than teaching them the skills they need. 
 

There’s a West African jumping game that’s as popular there as hopscotch is here. It’s a little like Rock Paper Scissors. You face your partner, jump up six times, landing on both feet each time. On the sixth jump, you land on both feet, but put either your right or left foot forward. One partner wins if both of you land on the same foot (both right or both left), while the other partner wins if you each land on different feet. It’s not only good exercise, but it also gets each person thinking about what the other one will do. For example, “I noticed that he put his left foot forward for two tries, then the right. Maybe he'll do that again.”

I think the Wii is a good game system. My kids have it at home. I don’t think you’ll get much muscular strength or aerobic activity from it, but it is physical activity. It’s like mowing the lawn for an adult. It won’t get you in shape, but it’s better than sitting around watching TV. For kids, it’s a good alternative to watching TV or playing video games or Monopoly or CandyLand. Even board games have more social interaction than many video games. My son often plays the Wii by himself.

The problem may be with the game, not your child. After all, we teach kids to share—except when you play a game like this. Then you’re supposed to push kids out of the way so you can be first.