don't know if kidding but any remix where the Song is simply sped up by some 20-50% is called Nightcore, regardless of what song or genre it draws from. Though maybe that's somehow Alvin's hobby or something. idk. The joke is that if no measures are taken to prevent this, like youtube does when you use its speed up function, all frequencies will actually get pitched up in step with the speedup, therefore making the songs key different and significantly altering the tone of any voice. (towards squeaky and excited)
Your example is from the '80s cartoon show, but Alvin and the Chipmunks are far older than that. They were a band (originally David Seville and the Chipmunks) formed in 1958, using a sped-up technique developed by David Seville (real name Ross Bagdasarian).
It did have a cartoon spinoff in 1961 named The Alvin Show, then later after David Seville's death, an '80s cartoon show named Alvin and the Chipmunks. And then in the early 2000s, a series of live-action/CG films.
When I was a kid (in the early '80s), my parents had several vinyl records of David Seville and the Chipmunks and I used to listen to them on repeat all the time. They also had a vinyl record of David Seville's "Witch Doctor" single, which pioneered the sped-up chipmunk voice effect. That song was an earworm! We'd be singing it for days after hearing it once. It's no wonder Alvin and the Chipmunks became a hit sensation.
I had a tape player that would kinda do that if you pressed fast-forward and play at the same time just right. I forget all the albums I tried that with, but the most memorable was Napalm Death's Utopia Banished.