Tapes may simply be an archaic term still in use that refers to newer technology, much like when people say they filmed something with a digital camera.
“Archaic” is a bit harsh, isn’t it?
(I mean tapes aren’t that old, and film is still used quite often.)EDIT:
Never mind, I just looked up the word and it does work for something only relatively old. There’s just something about “Archaic” that makes something sound so ancient.
We are talking about a universe where some people are using ancient weapons that are no substitute for a good blaster at your side. 😉
And maybe the Empire’s tech support guys are old geezers who still swear by tape backup drives, which made it easier for the Rebel spies to purloin a copy.