E.B.
I guess I would want to know a couple of details. First, how old were these kids? Second, were the kids playing at a normal play time (early evening, for example) or did this Nerf gun fight start at like 2 in the morning when the parents would normally be sleeping?
I agree that homeowners insurance should pay for damage to an $800 tv. Maybe the parents don't want to file a claim and pay a deductible, but that's their choice.
I don't see where you're entitled to the broken tv.
If your son is old enough to understand costs, and if he purposely threw the gun and is old enough to understand that throwing toys can cause breakage, I'd have him do some chores to earn part of the money.