Lots here to critique and learn from.
First and foremost avalanche training was clearly deficient and this drove everything else.
The group was only partially equipped and the guy who took charge was racked with indecision once he got on scene. His lack of preparation was glaring. Even if they'd had training the lessons weren't retained or practiced well enough to be relevant when needed.
One thing that caught my attention was the digging technique. Aside from the gloves/cold hands issue, the rescuer didn't know what to do. Now this is just a theory, but I think his sense of urgency was lessened a bit when it became clear the victim was conscious.
I was taught "Strategic Rescue Digging" or STRED for short, which is geared for a total burial but applies to most rescues.
STRED is best done with 3 or more people
Once the victim is located either by an exposed hand or foot or by probe hit, the team shifts a bit to the side and downhill 6 feet.
From there the digger 1 begins furiously trenching into the slope horizontally and uphill to the victim for 2 minutes. Digger 2 clears the snow pulled downhill by digger 1, and digger 3 is on standby to relieve digger 1 who slides into the 2 slot while digger two rests. The dig-rest cycle repeats until the victim is uncovered or the diggers are relieved.
This method allows the rescuers to use gravity to keep excavated snow out of the way
You never dig straight down to the victim because all you'll do is collapse more snow onto them, and as you get close compress the snow close to them possibly around their face and mouth.
Another thing I found disturbing (maybe I missed it) was the lead digger never asked to the victim if he could breath OK. Assuming he's conscious and there's no medical reason to leave them on...once his head was clear I would have asked him if he wanted his helmet and goggles off. I know I'd want mine off immediately.
If the victim had been a foot or two deeper this very likely would have had a tragic ending.
Never forget that every mistake is a potentially life saving lesson for someone else.