IIRC (and I was a cadet) route step was when you deliberately broke step to get out of sync with each other...the classic example for using this was when crossing a bridge. But these cadets don’t all have their heads facing forward - which indicates to me it was at ease march.
Never heard of “At Ease” march, but I have given the command “Route Step, March!” It is as you said, to break the rhythm.
How you can march a formation at ease leaves me at a loss.