This seems more like a PS2 model with PS1 textures (you have to remember that the PS1 was VERY limited, to the point where the bouncy animation alone would probably make the ancient console explode). Still, fantastic stuff! Maybe we could compromise and say this is something we would see on the SEGA Dreamcast or PC ports of PlayStation and N64 games at the time.
I'm overthinking this cute little animation, aren't I?