I doubt "Class M" stood for anything originally. As CorporalCaptain
shows, it was included in the original 1964 pitch document -- and there's a lot of stuff in there that Roddenberry just pulled out of his hat, like the alleged equation for how many inhabited worlds there might be in the universe, which was pure gibberish. So I'm sure "Class M" was just some random term Roddenberry made up to sound technical -- like the reference in the next paragraph of Captain April's orders, "You will patrol the ninth quadrant, beginning with Alpha Centuri and extending to the outer Pinial Galaxy limit." Let's see... not only is there no such thing as the Pinial Galaxy, but Alpha Centauri is misspelled, there can only be four quadrants, and two points only define a line, not a volume of space. But that didn't matter; what mattered is that it sounded like it meant something to the characters, that it gave a feel of the texture of the show's world.
More to the point, the pitch document wasn't meant to be published, it was just meant to sell the idea of the show to network executives, most of whom wouldn't have known a galaxy from an asteroid. So it didn't have to make sense. It didn't even have to accurately reflect what the show would become (or else we would've been following the voyages of the starship Yorktown
all this time). So "Class M" was just gibberish, like "Pinial Galaxy" and his ersatz Drake Equation. The only difference is that it's gibberish he decided to keep using. If things had gone slightly differently, we might be debating the etymology of "Pinial Galaxy" right now.