Our state has a 35lb minimum draw weight for deer hunting.
I watched that video and I think that bow is some heavier - maybe around 50 or more.... I didn't see the specs on it, just sort of judging by the sounds of the shot (twang of string to striking of target). Not too scientific, I know lol...
As far as your question, yes, I would say one could kill a deer with a 35lb bow. That said, I would say that everything would have to be done right, razor sharp point, good shot placement, and a 35lb bow which has excellent cast per pound of draw weight... Personally, I would want has much weight as I could draw on a cold morning before a warm up, and that I could shoot accurately. For me, that is high forties to high fifties. I bet if you took a poll on this site that you would find 90% of these guys hunt with bows between 45lbs and 55lbs of draw weight.