He manages to split HP because you didn't keep buying them, but greened early and started to choke. On turns 8, 9 and 11 you bought Province instead of HP.
He manages to get through the junk in his deck because Hunting Party gets through it pretty easy, and the extra draw from Alchemist only helps. HT helps too, because that junk becomes useful.
Also, Horse Traders is FANTASTIC for a Hunting Party stack. You will almost certainly have junk to discard (Curses and VP), +$3 is nothing to scoff at, and the +Buy is great for when you have extra money but aren't ready to buy Provinces yet. Consider turn 11 when delirious is able to buy HP AND Alchemist, or turn 22 where he buys Province + Duchy. I would have taken HT over Moneylender.
As far as discarding Curses goes, he discarded a Curse 5 times and you did it twice. Just bad luck. But on the turns he did it, he usually hadn't returned Alchemists. Just once he had returned a single Alchemist. The other times he did not.
I don't think Cellar is so great, but I'm not sure.
