The "DRM" acronym for Direct Rendering Manager goes all the way back to the 1999 Linux driver for 3dfx graphics cards. It predates the "Digital Rights Management" acronym by at least 5 years.
For what it's worth, the Oxford English Dictionary gives two citations for the phrase, one from January 1996 and one from May 2005. It's not obvious to me from the quoted text whether the 1996 citation actually has quite the same meaning as we're talking about here.
It's from something in PR Newswire, and it says: "As an industry consultant Bob has been a leader in developing business strategies and cooperative relationships in the area of digital rights management and content distribution."
And what's not clear to me is whether that's "digital (rights management)" -- i.e., using computer technology to enforce copyright etc., the usual present-day use of the term -- or "(digital rights) management" -- i.e., everything to do with handling copyright etc. in the specific context of digital data.