You're on the right track with guy being more more gendered than guys, but I wouldn't go so far as to say guys is completely neutral. Take "Guys and Dolls" for example. A very dated example, but that specifically-gendered usage does still exist to a reasonable extent, like saying "it's guys' night" and so forth.

Basically, guys is neutral in those cases where it's used to describe a group that isn't entirely male but otherwise it's male (somewhat circular reasoning, but I can't think of a better way to describe it); guy doesn't usually get that same logic applied.