This is untrue for the dps loss. Holding an ability to use it whilst moving is more of a loss then just using it as soon as you can within your priority.

Say ability X has a 5 second cooldown instant cast. Holding it even 2.5 seconds means you just missed out on half a recharge.

Doing this 4 times in the fight means you lose 2 entire casts etc.

Dps = damage / time.

You could have ability Y with 2 charges. You could hold the stacks till 1.99 and use them back to back and it would do the SAME dps as someone doing them 5 seconds apart. As long as you never cap stacks and as long as you finish on 0 you will do the same damage regardless of useage. (Simplified of course many things could change the ability damage)

But holding something past its cooldown is a dps loss unless you are holding it to gain more damage then you would lose from not casting that extra. Which is not the case during movment and is definitely not a protip for dps, it can smooth out your movment and some dps is better then no dps, just use what you can whilst you move.