Random_Coffee: Yes, you can redeem the game-code on your own account.
bruceFish: Cool, thanks for the quick answer! I will try it out this evening.
You should be aware, though, that if you choose to make the Mystery Game into a gift order before purchasing, it will draw randomly from the list of all available games in the pool -- even ones you own. If you just make the purchase normally (i.e., without marking it as a gift), the system will check the available pool of Mystery Games (some of which have limited quantities which are replenished periodically) against what games are on your Library shelf, and give you one you don't already own if it's possible at that time. If you already own a lot of the games on
the list, purchasing a Mystery Game as a gift will make it less likely that you'll get something you don't already have.
In general, though, unless you have a particular recipient in mind for a game (be it yourself or someone else), it is a good idea to purchase anything you're not sure you want to keep as a gift and send the code to your own e-mail.