It isn't knocked out by the fall, but with it already on the ground, Drake managed to keep it down long enough for you to finish binding his legs. After which Drake follows your example, letting out a few pants of fatigue, before responding, "I suppose it was... But damn, these things are strong... Never actually wrestled with one before... though I have seen them around." At your question, he answers, "Well... it's not mind control, but I can influence his biology to make him more passive, either short term or long term, with my blood magic. Alternatively, it is a pack animal so I can try to dominate it and make it accept me as 'pack leader.' I suppose you can try as well... but I'm not sure you can pull that off."
Spoiler (click to show/hide):
First is correct, second isn't. A Direwolf is basically just a very large wolf(Size of a horse, but with shorter legs so lower to the ground), and the reason it went on it's hind legs is because his head was pulled back and up. Partially due to being pull that way, and partially due to try to not to be choked by the rope, he ended up on his hind legs, but is poorly balance there(especially since they are bound together), and thus was able to be knocked over by Drake.
Random person in the comments section of a random hentai manga- "Now I am ashamed of myself."
Me- "Posh, shame is for fools and people with friends... we need no such things, we have the internet."