Is "Saw" a thriller?

Even James Wan says it is

The Argument for Saw as a Thriller

I recently read an op-ed in Creepy Catalog claiming that Saw isn’t a horror film, but is actually a psychological thriller. The author claims it’s closer to David Fincher’s Seven than it is to Hostel.

His central claim is that Saw functions as a thriller due to the mystery/puzzle element at the core of the film:

“Each of the films offers a mystery to be solved, while they serve as pieces of a larger puzzle. The first movie sets this all up, though, posing the crucial question: Why is Jigsaw doing what he’s doing? It’s not like certain horror franchises where someone puts on a hockey mask or a mold of William Shatner’s face and murders people because they’re – checks notes – simply evil. There’s a purpose to what he does and it’s about finding out his motivations here.”

He backs up his claim by quoting Saw director James Wan, who said in an interview,

“I found it really kind of lazy. Leigh [Whannell] and I took three years to write the script, to make this crafted thriller, but it seemed like everyone was focusing on the trap aspect of it.”

Even the Saw producer and Godfather of horror, Jason Blum, had this to say:

“The original Saw was really a detective thriller that happened to have two elements you don’t see in a traditional detective thriller: a huge twist and a gruesome premise.”

The author closes his argument by saying, “Put the traps to the side and take a look at the story to see what it’s really about.”

I agree! Let’s break down the story using the Horror Formula and see where it falls.