First, the evidence that this position actually works and has been used in practice comes from the 1942 book Get Tough! How to Win in Hand-to-Hand Fighting, as Taught to the British Commandos, and the U.S. Armed Forces by then-Captain W.E. Fairbairn. The technique is called the Grape Vine, and is described on page 37. The relevant passage can currently be read on this site.
Even though you have left your prisoner's hands free, it will, if he has been forced well down the tree, be almost impossible for him to escape.
I tried this with my friends back in my youth. The "average" person can't free themselves from this position. A friend of mine that weighed little and had strong arms, however, could pull himself up the pole with his hands and free himself.
A couple of us, myself included, stayed for quite a long time trying to get free, eventually lying backward with exhaustion. There seems to be no danger involved. The position is quite uncomfortable after you stop supporting yourself with your muscles, so probably blood circulation to the feet is partly restrained.
The possible causes of death from being in this position would be:
Hitting the head when falling backwards.
There's no easily conceivable reason the fall would be uncontrolled. If it were, the force caused by the fall is considerably lesser than when falling backwards from a standing position. It's not uncommon for this kind of fall to happen in boxing, but it's rare to die from that (at least one recorded case exists). So death from falling backwards seems improbable. Still, Get Tough claims that people throw themselves backwards and are killed:
Normally, the average man placed in this position would get cramp in one or both legs within ten to fifteen minutes, when it is not at all unlikely that he would throw himself backwards. This would kill him.
Lessened blood circulation to the feet.
This could eventually develop a dry gangrene, which "is usually not life threatening" (unlike other forms of gangrene).
If there's no water available, death from dehydration will occur in 2-10 days, depending on temperature. For death from hunger, see the question Fasting for 40 days - is it possible?
I'd say dying from thirst is the most probable cause, since that will definitely eventually happen.
The position is very easy and fun to try out for yourself in controlled circumstances with at least two friends. However, this is not advice to do that.