To be precise, you should define exactly what you mean by the "original state." This could refer to the intrinsic state of the puzzle (where the orientation of the cube itself is considered not to matter) or (alternately) if you consider the orientation of the cube as part of the state. If the puzzle has indistinguishable pieces (4x4x4 and larger), then the answer may be depend on what exactly the original state is (unless you want to consider the pieces to be distinguishable even though they may look the same). Commonly the starting state is taken to be a solved state.
As I understand, the MZRG order calculator (qqwref's) assumes the starting state is a solved state, and it counts how many repetitions are required to get back to a solved state, whether or not the cube has the same orientation or not. Randelhofer's applet appears to give the true mathematical order (meaning the pieces and their orientations are all distinguishable, and the orientation of the cube is considered to matter), as well as how many times the maneuver must be repeated starting from a solved state until again reaching the solved state with the same orientation (but indistinguishable pieces/orientations not necessarily in the same positions/orientations).
In any case, if I understand your 4x4x4 sequence correctly, it appears the answer 27,720 regardless of which interpretation you use for returning to the "original state."
Note that this may or may not ignore orientation; both can be useful.
As explained by Bruce: