They are but the recording is not: it's copyright belongs to the performer. Unfortunately YouTube can't figure out the subtle differences between performances that identify them.
The headline is slightly inflammatory in its reference to the "200 year old composition." Exactly to parent's point: a contemporary recording would be neither 200 years old not in the public domain.
I'm not sure I agree with inflammatory. It seems that the common attribute between the two materials is that it is based on the same 200 year old composition and not much else. Like if IT takes your keyboard and gives it to someone else because they are the same keyboard. Completely missing subtle differences like the serial number or the fact that on one the space is worn out and on the other the tab key.