Should a snowboarder in a closed area be responsible?

Most definitely.

The owner of the enclosed area might be partly responsible if the enclosure doesn't stop the avalanche, or for allowing snowboarding in conditions that could lead to an avalanche, but the snowboarder would still be responsible.

I would say IF it is a high avalanche area and the person knows that and is shouting and screaming to see if that person could make it happen in any way possible I would say YES.You just never know when one will take place you just hope that everyone will survive it. :)

It would only yield a dry judgment. If he survives bill him for his rescue and compel volunteer services for the rescue station - scrubbing toilets, shovelling the airfield, that sort of thing on weekends for the entire winter season next.

If their actions can be proven to be at fault, certainly. And for the cost or search and rescue if they need it.

It is sad, but that young man will likely face charges of involuntary homicide.