Babcock is an excellent coach. But there are many excellent coaches. Strategy wise there is nothing special, and yes many if not most teams employ these same strategies just as effectively.
the one edge that babcock has on many of them, which is especially important in Toronto, is that he is a natural leader that commands respect. his players trust him and listen to him. horachek used largely the same systems, but nobody listenee or believed in him. and unlike some, he doesn't need to use fear as a motivator. he is strong but supportive and fair.
but strategy wise, Babcock is no mad genius. just one of many smart coaches. he might have a better natural in game feel for matchups and hot hands than many, but that's probably not a huge deal.
No, the biggest factor here is that Randy Carlyle was an absolute disaster of a coach. He made the players on this team look worse than they ever had under anyone else, and he fact that they are now looking like competent even good NHLers now under a normal system is making Babcock look like a magician.