You could probably check this at home by taking the side cover off to confirm there is a gap between the end of the valve stem and the tappet when the valve is closed. I say probably because it isn't clear in the video if that area can be reached with the valve spring and keeper in place. If it needs to be adjusted though that's a fairly major disassembly.
If the blade is not directly attached to the bottom end of the crankshaft then it's unlikely the flywheel key has broken. They're designed to break away to reduce damage when the blade is directly attached and it hits an obstacle.
If the blade is not directly attached to the bottom end of the crankshaft then it's unlikely the flywheel key has broken. They're designed to break away to reduce damage when the blade is directly attached and it hits an obstacle.