Ultimate adds BitLocker (Hard drive encryption), support for Networking Domains, the ability to back up to somewhere on a different network... etc... None of these things are necessary (or even desired) for a gaming rig.
I would also like to point out there are other programs/options if you decide you need X feature later on. For example, for remote desktop I've started using logmein, which is free. If you need to encrypt a harddrive I've heard many good things about TrueCrypt. The XP mode found in the higher versions don't allow for video acceleration so gaming isn't possible. You might be able to find a VM program that allows the same thing however. (virtualbox?) As you can see MS includes many extras in the higher version, but you can find similar (and free!) just by looking around.
Edit: Forgot to mention that I don't know of any other way to join a domain. If you need that functionality then you'll need the pro version. If this is a straight gaming build HP will be fine.