Hard to say w/o seeing it, but I'm guessing it was an amble (4 beat intermediate gait) as that's most often what's done by non-gaited breeds. The running walk is specific to the TWH.reminds me of an Arab I trained and he did a normal walk/trot/canter/gallop but then he had a "running walk" as well. Not sure what it's really called but smooth as butter, a very fast ground-covering walk.
Pretty cool when a non-gaited breed does a soft gait! I've heard of it in (rarely) QHs, Morgans and Arabs.