Sorry, I don't see the irony. Anyway, having ''The'' as an honourific for band names was commonplace in the UK prior to the '70s, even if the band's name had not been stylized with "The".
Again, for people of a certain age or generation it was commonplace to prepend it. I find it endearing in a nostalgic way. I can infer from that person's use of it that he is of that age or generation.
Ever see someone mention "The Donald"? It's the same thing.
It's when something or someone gets so recognizable that they can be referred to in a singular sense. There are lots of instances of this throughout pop culture.
In the context of the interview, it's someone who was part of the "Floyd-verse" (this word is a mashup of Floyd and Universe, another common affectation). Pink Floyd was a remarkably famous band, and they still are. Someone that was part of the "Floyd-verse" naturally would have felt the band as all encompassing. It wasn't just a band, it was tour after tour, hit song after hit song, millions and millions of fans - and getting caught up in that made "Pink Floyd" seem far bigger than the sum of its parts. Calling that phenomenon "The Floyd" is actually very succinct, and portrays how large a cultural phenomenon Pink Floyd was and still is, 60 years later.
I have to wonder why you can't/won't understand this.