It is definitely lazy fight choreography, and especially unevenly applied here, but that totally does happen. Not to go all bouncer, but we are so fragile if we are hit in the right way. A broken jaw or a good, undefended strike to the temple or upper head area can immediately bring down even the biggest toughest guys and even prove fatal.
I guess what I'm saying, though it chagrins me to no end to defend the fucking Karate Kid, is that we can assume that Mr. Miyagi is such an expert that he can apply those kinds of blows to these kids, and we are watching through young Daniel's perspective; so given the shellacking he just received, he probably isn't very precisely registering what was going down.
I mean that's what you would say if you felt the need to justify your simple suspension of disbelief while watching a movie when you were a kid.