The only reason I can see 'the' isn't before 'planet' is that it wouldn't sound nice in the title. The studio probably thought that "The Planet of the Apes" would sound less catchy.

hi, "the" before apes means that in this context, these are no apes like any other, but a specific type of apes, unlike other apes. the word planet however is not specific, it could be any planet, and is insignificant to the context.