MR you are right, the rears should be driving the tractor up the hill, but the loading on an empty PT is such that there is more weight on the rear, so the fronts will be the first ones to spin. (Same torque, less weight, therefore less friction, so first to spin out.)
I can't tell from the video; is that wide ope throttle? The engine sounds OK from the video, just not full speed. Nevertheless, if the pumps and motors were engaging, I would expect to hear it bog down, and it doesn't. See my prior post for ideas on root causes.
I don't know if it helps, but here is a little on the function of a variable displacement pump. If you want to look at how the drive pump for the PT functions, look at these links;
Axial piston pump - Wikipedia, the free encyclopedia
I'm a slow learner sometimes. It took me a time to unlearn "stomping" on the treadle for more power. For PTs, when you need more power, you need to lighten up on the treadle to devote that HP to less oil. When the treadle moves, it moves the swashplate on the main drive pump, which is a variable displacement pump, varying from 100% reverse to 100% forward. There's a nice animation here:
http://www.youtube.com/watch?v=2mh902AP7Yw
Basically, the power that we have to work with is set by the throttle, and then we get to choose whether we want a lot of power in a little oil (e.g., 5% treadle, WOT) for hill climbing, or dividing the HP over lots of flow (treadle to the metal) for full speed on level ground.
All the best,
Peter