Maybe spoilers below?
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I agree with you about FINIS being unintuitive. I Thought it was trying to say FINISH, and that I somehow missed the H.
However, I interpretted GAE as an alternate spelling of gay. I don't know what the definition of it is referring to though.
Also, since you mentioned "The Witness", you might also like "The Looker". It's not as long, but it's a fun parody of "The Witness", with a similar art-style & gameplay mechanics!