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.
https://www.youtube.com/watch?v=NPLQLUqB-fo
Here is a Dromedary camel walking using the 2 legs moved at the same time on one side type gait.
https://www.youtube.com/watch?v=Svt5BpwxAfk
(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)