Alligators do indeed eat fruit and leaves, in addition to the various meatier things they use to sustain themselves . . . like small dogs. But somehow, I don't think this is quite what Mother Nature had in mind.
Rest assured, though, that the watermelon will not hurt the alligator. This 'gator's name is Doofy. He belongs to Gator Adventure Productions. Reportedly, Doofy and the company's other alligators seem to enjoy crunching up the watermelons in their big gator jaws, and seem to anticipate the game with what appears to be pleasure. Young alligators and crocodiles have indeed been observed to play, so it's no surprise that Doofy gives that happy little jump in the air, just when he's about ready to glomp. It's just sheer enthusiasm for watermelon-fetch. Either that, or he's planning to make a respectable carnivore-style grab for the handler's arm, once he's had enough practice.
Although there's still a good deal of debate about whether or not crocodilians actually need some amount of fruit in their diets. They've been observed quite deliberately eating various fruits and vegetable matter both in the wild and in captivity. Apparently, researchers originally speculated that the plant matter had been ingested accidentally. Other researchers suggest that, at least in the case of captive alligators and crocodiles, the behavior might be learned from other nearby reptiles and amphibians.