What would they get out of that? Not a Trump presidency.

Trump and Putin actually seem to have a very good relationship and have spoken positively about each other. Trump winning could legitimately foster a new era of better relationships with Russia.

Hillary would probably be the opposite.

What Putin says, largely for domestic consumption, and what he truly feels, are, I quite strongly suspect, rather different things.

Adam Curtis has touched on this, in "Bitter Lake" IIRC. Recommended. (BBC video documentary -- this bit comes early on.)