It doesn't look like that POS could get rid of that stump even if he were on flat ground.
Having used my stump grinder on the PT-425 a lttle, I've found the PT stump grinder actually works pretty well, if used correctly.
What you're seeing here is a couple things, IMO:
a. Inexperienced operator having a hard time keeping the machine positioned on a slope, as previously mentioned.
b. A side-effect of the PT's lift/tilt controls being VERY, VERY sensitive when operating at full throttle (which is needed to give sufficient power to run the stump grinder).
The 30-HP machine probably only gives about 15-18 HP (if that) to the hydraulic PTO, so you can't jam the stump-grinder down into the stump -- the hydraulic motor will stall -- which he does repeatedly.
Yet, the controls are so sensitive at full throttle that it is a challenge to "lightly push" the stump grinder down onto the stump and hold it there while it grinds. Then, you have to maintain that while articulating with the steering wheel to sweep it side-to-side.
Watch him repeatedly put so much down-pressure on the grinder that he's lifting the front wheels -- in one view, the front wheel is spinning while he's grinding...
I've found the stump grinder to be one of the most challenging implements to use, but it works pretty well.
Like using my brush-cutter, it may not be pretty to watch, but it produces nice results. After many hours of using the brush-cutter, I still will lift a front wheel frequently when I set the cutter down (having lifted and carried it), because I'm running full-throttle and I can't go past down to float position fast/smooth enough...