Mirror Coat isn't really a move that's made with mirrors or barriers. Just like with Counter, as shown by Wobbufett in the animé, Mirror Coat is a cytoplasmic coating that covers the user like a jelly, and anything that hits it that's special-based, gets absorbed and shot back in a more powerful way. Of course, this is misleading, as it's shown to be a mirror-like animation in the games. I'd say Game Freak either overlooked this move for Mr. Mime, or actually thought it'd make little sense, if looking at the Animé.
It's sort of a stretch to use this as an answer, but it wouldn't be the only time Game Freak took a page from the show to make something canon.
