Watched it three times and yeah, something's definitely there. The movement pattern is what gets me - it's not the typical lens flare or shadow cast by a moving light source because the trajectory doesn't match anything in the frame. Proper translational movement with no corresponding light shift.
That said, Waverly Hills footage gets picked over constantly and a lot of it does turn out to be investigators walking past doorways on different floors. The building's layout means you get some genuinely weird sightings that are just line-of-sight artefacts.
What timestamp are you working from? There's at least two bits in teh main circulation video that get conflated all the time. If you're talking about the 34-minute mark clip that was posted on YouTube about two years back, I've got some thoughts on that one specifically because the motion profile on that shadow is genuinely hard to dismiss. Would like to hear what others make of it before I get into the technical breakdown.