Short answer, probably not as a whole, but the Real Money Auction House is unprecedented legally
Zynga would like a word with you, as would a lot of pay-for-item games on Kongregate.
With the RMAH, ActiBlizzard tacitly endorses its virtual items as having monetary value, and encourages players to exchange those items with each other while profiting via a transaction fee.
Because they'd rather get the transaction fee than Paypal, and since the transaction happens within the game, there's no possibility of fraud between players.
1) What can and can't ActiBlizzard do to affect the value of its items? It probably can't shut down the game,
Tough call. My suspicion is that with a certain amount of notice--say, six months--they could shut down the RMAH for those six months, then shut down the servers, and a challenge wouldn't hold up legally in court. Note, though, that you can still play D2 online, and original Brood War as well if I'm not mistaken. Blizz isn't likely to shut down servers unless they go bankrupt.
and it probably can't have its employees selling stuff in the RMAH.
Depends on the employee. Their CMs and GMs generally won't have the ability to spawn items. I'm betting, though, that the employees probably are locked out by Blizz.
Can it nerf items?
Yes. Hard to claim that's an overreach of the EULA.
Can it "purchase" items off of the Gold AH to stem inflation if it would shrink supply and drive up Real money?
Yes, just as Blizz could create items and sell them; again, cf. Zynga. My guess is that neither of those would be a good idea; if they decrease inflation by buying items, that item cost is going to players and might not be made up for by increased trade fee revenue. Likewise, if they create items and dump them on the RMAH, they'll make money in the short run, but cause a drop in market prices that might decrease trade fee revenue in the longer term. Were I Blizzard, I would
not want to speculate on that sort of thing.
Is Diablo 3 subject to gambling regulation as a game of chance? The game involves some skill, but it's very loosely tied to the quality of the drop.
Tough call there, I lean toward no, for the simple reason that it is impossible to
lose the game of chance. The only way to lose money is to buy something. The game of chance portion is more akin to "Hey, here's a big bowl of stuff. Grab something random, it's free to try your hand! If you can sell it to someone, great! If not, well, um, anything free is worth what you paid for it..."