This is the position of everyone when the first shot is fired (assuming there isn't some delay between audio and video on the YouTube clip):
That may be 10 feet at the most, but I wouldn't call it 10-15 feet. Assuming the officers and the suspect are all anywhere from 5'6" to 6'0", that's probably 7-8 feet.
The suspect started walking toward them at a faster pace at this point, which is what caused the officers to fire.
I don't see his hands raised, but aside from that conflicting with the officer's report, I don't see a difference. They know he has a knife. They know he's closing the gap between them. Hands up or down, he's a threat.
The situation could have been handled differently, but I don't necessarily see anything wrong with the way it was handled. Maybe the guy wouldn't have responded aggressively if the officers hadn't immediately pointed their guns at him, but when there's a guy on the street with a knife acting suspiciously, I'd rather the officers immediately have the ability to neutralize the lethal threat, rather than start the situation unarmed and risk their own lives or the lives of bystanders.
As far as how to neutralize a guy with a knife, and whether something other than a gun is just as or more effective, I'll leave that up to those who work with those weapons and train people to respond to these situations. Personally, I don't own a taser, but even if I did, I would have no issue with shooting a guy who has a knife and is approaching me. And legally speaking, I'd be in the right to do so.