Here's the thing, the Predator doesn't do what he does because he's an operator on a mission, an operator on a mission would aim for the upmost efficiency, not wasting time or effort on his kills.
The predator isn't an operator on a mission, he's hunting, if he's hunting that means he's doing it for thrills, he finds enjoyment out of it, and many of the things he does to scare his prey aren't the most efficient ones, because there's no fun there...
He could've killed Mac right then and there, instead he flashed him and left him with his brain scrambled, he could kill Dillon right away, instead he chopped his arm and killed him with his blades.
There is no way that doesn't denote personality.
And the fact that he laughs at the end, he's a smart creature, he knows what laughter is, seals the deal on the premise that is a personality.
It's an intelligent creature, it's also savage, which manifest in it saving trophies, how on earth is none of that a personality?
Oh, another proof of personality, the fact that he removes all his weapons and mask to face Dutch... A tactical decision is supposed to save you time and effort, not do the opposite, this was pure thrill, enjoying thrill is a personality trait.