Unless we are redefining "theft" - this indeed is not theft, but copyright infringement.
In the "singular" case, there may not seem to be so much difference, but consider an individual "downloading a copy of every song and bit of software in the world" compared the same situation, but taking without leaving a copy in place.
Copying - there is no noticeable effect on the "victims", Stealing (particularly if you include all backups) is a global catastrophe.
That said, as this concept seems unclear to begin with, and we've had various actors intentionally blur the lines for quite some time, perhaps it does make more sense to redefine the word, perhaps pick a new word for the less-common offence previously known as theft.