There's always the possibility that they're some other kind of storage medium but everyone just calls them "tapes" out of old habit, much as we may still speak of "taping" a show off TV, or for TV, when it's not really tape being used. (Like "dialing" a phone number when there's no dial.) That would, of course, require that tapes had been used fairly recently as a storage medium, which we would have to imagine being necessary for some science-fictional reason. But once you've done that, why assume they're not still using tapes?
We never really get to see if there's actual tape inside. That said, I very much like the idea that there is.