In a medieval European style forest, this would be super useful for hunting. Mainly because prey animals don't look up! There's nothing native to Europe that would attack, say, a full-grown deer or wild boar from above. That goes double for forested areas. (There may be a species or two of eagle that could snag a smallish deer/young boar from the air, but they'd need altitude for that and therefor attack in clearings or grassland, not woods. I know these exist in the world but am unsure if any euoropean eagles fit the bill.) So if you get 20ft+ up/down a tree with ease you can visually hide from most of the "big game." Against smaller things like rabbits this isn't really useful, but nobody gets famous from hunting rabbits! Plus that's an extra 20ft+ of being "away" from your target as far as scent goes. But as you said, that's the same sort of benefit you'd get if you got into a tree at all. So what does doing it well/quickly get you?
Even if he can't tarzan-jump from tree to tree with ease, getting DOWN from his tree safely at speed provides a huge advantage over a tree-stand hunter. A big problem with tree stand bow hunting is if you don't get a one-shot kill the prey takes off wounded, and then you have to laboriously climb down and try to follow it. (same for guns, you're just more likely to kill the thing in 1 shot with a gun.) Sometimes you never do catch it, maybe it died in a place you can't find, maybe it survived its wound (for a while anyway) and got away. But if you could go from 30ft up to ground level in a matter of seconds you could pursue on foot and have a higher chance of finishing it off/finding it when it finally collapses and dies.
If he CAN Tarzan about tree-to-tree with ease he becomes a REAL good bear hunter. Bears up to a certain size can climb trees (the American Black Bear is well known for it) but they can't jump between 'em. Stalk your bear, fire an arrow, and when it chases you flee up a tree. Bears go UP trees fast, but down trees slow. Your hunter would run up one tree, bear follows, he jumps to another tree, and finishes off his target. Much safer than trying to take out a bear on the ground!
There might also be a benefit (depending on his skill) for stalking prey. Again, most big animals (humans included) don't naturally look "up" when scanning for danger in a forest. They also expect a certain amount of noise from birds etc in the trees, so he needn't be silent. He just needs to get up a tree, not make a TON of noise, and move tree-to-tree stalking his prey. Deer doesn't look 30ft up (because it's never had a serious threat from above) so deer misses your hunter getting close. Then it's an easy bowshot/spear throw from above at the unsuspecting target.
As a side-note these skills would also translate into him being a crazy-good scout or ambusher as well. The big problem for shooting at people (who shoot back) from a tree is that once they know you're there you're basically dead, as you can't escape quickly. Your Great Hunter however WOULD be able to escape quickly, making him a real pain in the rear for an opposing force in the woods.