Will giving out the following pose a identity threat?

There's a website called gamevance, you play games on it and if you have the highest score you'll get your choice of gifts. I have friends that have gotten gifts from the site so I know they're legit when it comes to paying out the rewards. Though I also know they require you to install their gamevance program even though your just playing web browser flash games, it's a virus. Though I know how to guard against viruses, the site requires you to give them your real name, address, home phone, and when you win a prize the first time you must verify that it is indeed you by taking a picture/faxing your drivers license.. Is it possible that with these info they can steal my idenity? I know that the most important ID is your SS, but I'm still a bit weary that this company knowingly installs a virus on their members computers. I plan to call the company tommorrow and ask if I'm able to black out my drivers license number.