I saw during the ESO Live demonstration that the new Camel mount (and I think camels are adorable!) doesn't walk/run like a camel does, it looked more like a horse gait than a camel gait.
Camels tend to move both legs on one side at once when running (pacing) and can do either the both legs one side or the more horse-like walk when moving slower. They tend to look pretty goofy when moving fast, but it is part of what makes them so cute!
I couldn't find a really good clip of the Dromedary camel walking and running but did find this nice slow motion of a Bactrian camel (2 humps) running.
Here is a Dromedary camel walking using the 2 legs moved at the same time on one side type gait.
(It would be awesome if their idle animation would be to sit down and get back up since they stand up back legs first, front legs second)