One side of the coin suggests:
It's a 'creature-feature,' which is a popular subcategory of horror in general - and for that reason alone, it is under the Umbrella of Horror as one of the greatest of all time.
The other side of the coin would say:
The Speilberg-ian side of it leans more into "thriller with action/adventure elements" than outright VISCERAL horror. Like Jurassic Park, we have elements of high-stakes presented in an often terrifying life-or-death scenario, but you can say the same thing about Die Hard, so what differentiates it?
Well, we all know horror is a super subjective genre BUT my basic rule-of-thumb is:
"(A) If the plot is meant to evoke emotions like shock and fear,
(B) And its characters involved in interacting with the thing that drives the narrative like a person/creature/device are also filled with emotions like shock and fear,
(C) And the imagery is specifically crafted to have a response of emotions like shock and fear, whether literal or psychological... then you're most likely watching a horror movie."
Jaws fits that bill in all 3 regards.
A - Shark attacks
B - Characters are afraid of shark attacks
C - The depiction of those shark attacks
= Horror