DO NOT WATCH IF YOU ARE AFFECTED BY FLASHING LIGHTS
These techniques are the Rider Punch and the Rider Kick respectively, coming from the infamous Kamen Rider franchise. Common finishing moves by numerous Riders.
This example comes from Kamen Rider Black, which, while not the earliest example, it still predates Smash 64 by a wide margin. (That, and it's the only vid I could find)
This is not the first time Nintendo has made a reference to Kamen Rider, however, the only other example that comes to the top of my head is the Animal Crossing song, Go K.K. Rider!, which was done in the style of various tokusatsu shows from Japan. But the fact it's K.K. RIDER, and the motorcycle in the beginning of Brawl's version stands to reason that Kamen Rider was the biggest influence.