To me the important word was always "propelled". The language about a distinct kicking motion is useless. There's plenty of reasons a player might move their leg in what could be described as a kicking motion, without kicking the puck.
I think the question is did the player propel the puck into the net, as in imparted energy on it toward the net, or did the puck's own momentum carry it into the net after a deflection.
I don't think the Rangers call was particulary difficult last night. It's a small movement but IMO it's clear that the puck is propelled by that little knee flex right at the point of contact. The pass didn't look hard enough to cause that deflection.
The other two clips in that tweet are murkier. Players are allowed to move their foot into position for a deflection.
The Stone call is as close as can be but I'm guessing their judgement was that he extended his leg before the puck got to his skate, by the time of contact his leg is already outstretched and the puck's own momentum carries it into the net.
I think Mangipane is a bit clearer but still close. Yes, he's kicking his foot out toward the net, but the puck is deflecting off the side of his skate so that movement wouldn't be propelling the puck. Looks like there could be some sideways movement toward the puck but it's hard to tell with that terrible replay angle.
