In Brazil they might call that a marcha batida
It's a diagonal gait with some "disassociation" meaning that the trot is "broken" by the rear landing before the corresponding diagonal front. Properly done you get three feet on the ground at all times.
The "Indian Shuffle" is just another name for this particular point on the continuum of soft gaits. To call it an "Amble" would be correct, but the term "amble" usually is used in a broader sense meaning a non-trotting, intermediate gait. I guess of you "capitalize" it you claim it for yet another point on that continuum!
What does the horse do under saddle?