"They left him for dead" is idiomatic and quite common in English literature. It does not mean that the person left was dead, but that he was left in a state in which death seemed likely, or they wrongly assumed he was dead. It is as if he was as good as dead.
A comparable sentence to "they left him for dead" might be "they took him for a fool", which means that "they" wrongly assumed he was a fool.
"They left him for death" is not something I have ever heard. Sometimes in literature "death" is personified, either as something like the mythical "grim reaper" or just as a metaphysical conceit. I suppose that if it was your intention to suggest that somebody had been left for a personified "death" to come for then you could use this, but it is not idiomatic and so my short answer would have to be that this is not correct. "Dead" is an adjective, whereas "death" is a noun (the state of being dead) so you just as you would not say "he is death" to mean they are dead, neither could you say that someone was assumed to be "death".
Lastly, if there is no assumption that the person is already dead and has been left "dying" (but it is assumed that he will die), the idiomatic phrase would be "they left him to die".