Clue tokens may provide vital information about the weaknesses of your adversary(whether monster on Ancient One). When you run out of clues, you become clueless as to how to defeat whatever/whoever you're battling, so you give up the cause and lose.
Monster trophies are decoys for the likes of Shub-Niggurath and Thsathoggua. They eat up the dead monsters instead of killing you.
Gate trophies represent lore about the particular gate you've closed and the world it led to, and thus provide insight into the alien nature of Yog-Sothoth and co. as well as the AOs' weaknesses. Sort of like clue tokens, you could say.

