Actually, it's not really all that uncommon for Arabs to be gaited. It's certainly more common for an Arab to crop up naturally gaited than it is for say, a QH to "magically" be gaited. Of course, the AHA views gaited-ness as a pretty severe fault so it's kind of a "taboo" topic.
My mare (an Arab with the outside chance of being a QH/Arab cross) is gaited. However, she's not well gaited or anything, she's just mildly gaited. One of her ancestors, on her dad's side, was so gaited that he was actually double registered as a purebred Arabian first, then inducted into the TWH registry for "superior gaiting"!
Both these purebred Arabian gentlemen are clearly gaited (Rabiyas - just look at that picture and Bazleyd - the Arab who is also a TWH, haha!): Bazleyd Arabian Rabiyas Arabian
Anyway, Gallop On, I'm terrible at identifying gaiting from videos... I didn't see any "weird" foot movements but you never know.
My girl gaits very rarely so I have pictures of her gaiting and I've seen her do it but I've never gotten lucky enough to get a video of her doing anything but a trot.