In retrospect, it's a little funny that I read Dance Dance Dance ↗ before this book, its ostensible prequel. (There is something about Murakami's work that makes it easy to ignore pretext and prelude: a narrator says "this is the Dolphin Hotel, the place where I lost Kiki" and you kind of say, well, okay, that's really all the alienating table-setting I need!)
My perception of A Wild Sheep Chase — Murakami's third novel — is that it marks the shift away from his realism (later revisited in Norwegian Wood ↗ and Colorless Tsukuru Tazaki and His Years of Pilgrimage ↗) towards the surreal postmodernism for which he most famous and perhaps most revered, and in many ways this is a bit of a turning point. It reads very much like a noir: the journey to Hokkaido and to the Rat's house is propulsive and gripping and the mood of the book growing inward and claustrophobic is well-executed in a way that I think Murakami's later work often fails. The surreal here is not meant to be an object in of itself, or a force that creates mood in an otherwise placid scene.
His character work — always a pain point — is particularly rusty, though. I am glad he gave up his shtick of anonymous characters; it feels almost too on the nose, with various deutoragonists feeling like half-baked noir stand-ins than serious forces of agency or independence.
All in all: I think it's hard for me to recommend this, just like it's hard for me to recommend most of his ouevre. Which is not to say it's bad — it's not, and I had a good time — but it's Murakami bingo, for better and for worse.