> he has to use anachronistic cassette decks to play the tapes, which get converted into digital files

Anachronistic?

It seems like a complicated way of saying "the tapes were digitized".

Yeah, anachronism means 'not belonging to the time period'. If you made a 1980s movie and had the protagonist transfer cassettes to a laptop via USB interface, THAT would be an anachronism.

I think the author meant "old-fashioned" or "obsolete". Though using a cassette deck to read cassettes, geez, what else are you going to do? Build your own using an Arduino?