[JTBooth]

My guess would be that "a recording" in this case is actually an internal URI pointing to the show plus a start and stop timestamp. If YouTube wanted to not destroy those "recordings" they'd have to find somewhere else to store all the data.

Is there a way to download the recordings?

[DannyBee]

It's almost certainly about legal rights, not about storage of data.

[JTBooth]

Half agree. Probably they no longer have the legal right to store (and serve) the data. Which means that they cannot serve the portion that is between your timestamps, which they called a "recording" for reasons.