I don't think you watched the video. They weren't told to evacuate. The passenger saw the rotating red beacon, decided it was a fire, opened the door and initiated the evacuation without instructions or any crew input, all while the engines were still running. This should very much be blamed on that passenger.
Edit: I did watch the video but posted this before the post above was available. I think we agree that the passenger messed up but the crew is responsible for qualifying the passenger. This discussion seems to be about whether a qualified person did the wrong thing or was the person not qualified. My position is that the passenger was poorly qualified by the crew. Rhino's position appears to be that the passenger was qualified but messed up. This is a difference of opinion and neither is necessarily right or wrong.
The point I wish to make is that the passenger briefing card is there to qualify all passengers to be able to open the exit
when appropriate. Opening an exit into a known or suspected fire is contrary to the printed directions. The passengers actions were clearly wrong. With hindsight, the passenger should not have been seated in the exit row but it would be difficult for the cabin crew to determine that. I suspect that (poor choice for exit row passengers) happens all to often but fortunately aborted takeoffs at night are not all the common.
Now to the previously written post.
Rhino; You do not get it.
There is no doubt the passenger actions were not appropriate in this situation The question is why were those actions taken in this situation. He clearly made a poor decision and that was likely from poor training or misunderstanding combined with a dose of fear and confusion. He clearly should not have exited into a known or suspected fire with engines running.
I can name several accidents where numerous people perished while they waited for someone to tell them what to do! The point of the post is that crew members need to have the training and authority to do what is necessary and appropriate. The passengers in the exit row are accepting the responsibility of an additional crew member or if you like a crew member assistant. They do not need to wait for the flight attendant to come tap them on the shoulder and say "You may open the exit now" although it would be nice if there is a surviving crew member to make that call.
Read the emergency survival card next time you board an airliner and tell me where is says. "Do not use the emergency exit (or seat cushion or under seat flotation) unless commanded to do so by the captain or other crew member."
Please if you disagree do not say yes when the flight attendant asks if you will accept that responsibility. If you do accept, and it is not clear, ask specifically about under what conditions you should open the exit. The typical answer will be in the "event of an evacuation" with little or no explanation of what starts the evacuation. Typically that would be an announcement from the captain or cabin attendants. The passenger is not expected to start the evacuation in controlled "normal" situations but need not wait for directions when there are gaping holes in the fuselage with water or worse coming in IMHO.
Typically the modern airliner has a button at each cabin crew position to alert the cockpit that an evacuation is taking place. The first action for an evacuation is to push the evacuation button. That should put all crew members on the same page.
In an abnormal situation on the ground the first action of the cockpit crew, if appropriate, should be to make a PA announcement "Remain Seated" before the aircraft comes to a complete stop. You will frequently hear that as the aircraft approaches the gate but needs to stop short of the gate hold line.