The short answer is yes and no. Your iMac has the ability to run Windows however you need a license of Windows (XP of Vista) that you can install on it. You can install it several ways, Leopard comes with Bootcamp, the link below has some information about how Bootcamp works:
http://www.apple.com/macosx/features/bootcamp.html
The upside of Bootcamp is it is free, the downside is you have to turn on your iMac in either Leopard or Windows but you cannot turn it on with both simultaneously.
However if you purchase Parallels or VM Ware's Fusion (both relatively inexpensive) you can run Windows side by side with Leopard and move compatible files (an example is MS Office) back and forth between the two OS's. Again you need to have a license of Windows to install. The performance with either is excellent, I happen to run Fusion and found it MUCH faster than the PC I replaced.
However before you decide to install Windows on your new iMac take some time and decide if it's something you have to do or just want to do. Whenever you install Windows on a Mac your are turning your Mac into a PC so it's going to come with all the issues any PC has such as vulnerablity to virus's and other malware.
You mention you want to run games, if they are Windows only games they will run however which path (Bootcamp, Parallels or Fusion) I can't say would be best for your needs.
Again I'll ask if you have to run the games in Windows, before you take that step you might want to check and see if the games your daughter has will also run in OS X (check the games manufacturer) or if there is a substitute that runs in OS X.
Hope this helps,
Roger