Since like, the 70s

Have they not always had them?

This is tabletop RPGs, which, yes, do have DMs

The RP stands for role playing, like actual role playing. This was the term for tabletops long before things like Final Fantasy existed.

When the game is D&D?

Gives new meaning to "sliding in to your DMs"

Since every single ttrpg out there is hell bent on giving the “MC” a completely different name in each and every one of them, we'll just grab the most popular term and roll with it.

Also, this ttrpg concerns Tiamat, that one calls it a DM