Depends on what you mean by legitimate 8-bit. As far as the bitrate goes, it’s irrelevant: they’re unrelated factors (or close to it). What you might mean is the sample size, that is, there are only 256 possible values for each sample to be (bitrate is sample size * samples/second, you can get a 1 bit (sound on/sound off) sample to be at any bitrate you want just by having enough samples.) In that sense, it may be.
What people normally mean however, is “does this conform to the rules of some 8-bit computing platform”, and the answer to that is no, not for any platform people think of as being 8-bit. The generated waveforms are pretty clearly meant to sound like the NES, although its use of samples, actual recorded sounds, are too numerous but their quality is about right. For a good feel for how the music that made the best use of the NES sampling abilities sounded like, look up Sunsoft titles, particularly Blaster Master and Journey to Silius. Sunsoft was really the only company to make full use of it, everyone else just used the PCM channel to get better sounding drums, basically.
However there is one 8-bit system which fits the bill here! The only problem is that it was marketed as, and generally seen in the public consciousness as a 16-bit system: the TurboGrafx-16 (PC Engine for non-Americans.) This system had an 8-bit CPU but a 16 bit GPU, and audio capabilities more in line with the 16 bit consoles; I see no reason why you couldn’t create this song using its sound hardware (look up the L-Dis soundtrack for a good example of what the console can do.) Of course, the TurboGrafx was also one of the first consoles to feature a CD addon, so you could always just burn the music to a CD and play it back that way 
EDIT:
Sorry! The game that I picked to plug for the TurboGrafx-16 example is actually a CD game. Here’s a compilation of HuCard games, ones which used the internal sound synthesis:
