And thus the question whether the randomized way in which the player acquired the Sword of Uberness is a form of gambling is valid.
I disagree with this interpretation. Wikipedia's definition, which I think is a good one, states:
Gambling is the wagering of money or something of material value (referred to as "the stakes") on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods.
The wager is the important part of gambling, and that's the part that Diablo 3 is missing. When you go to kill a boss to get a random drop, you don't bet anything. And you don't lose anything. Sure the reward is random, but there is no loss, and no initial bet.
You have to be able to lose your stakes based on the random event for the activity to be considered gambling. In a lottery, you have to purchase a ticket, and that's your stake. Losing that stake, tiny as it is, is what makes a lottery gambling.
Where you can lose money is in the buying and selling of items. But that's trade, and it's not random. Sell at the price the market will bear, and don't purchase over-priced items. In fact, if you never buy an item, and always sell at below market prices, I don't see how you can actually lose money in D3. You may end up only making a tiny amount, and the amount per hour will be orders of magnitude less than a real job, but there's no actual loss.
But without the wager, without the bet, without the possibility of loss, there is no gambling. Diablo 3 doesn't make you put down wagers on what the random loot will be, and thus is not gambling.