Passenger compartment is even more wrong than glove box, though, isn’t it?

That compartment is used by the driver. I’ve never seen a passenger use it. And obviously, the driver doesn’t keep passengers in that compartment.

It’s got nothing to do with passengers, other than being on the passenger’s side. And if it’s really just because it’s on the passenger’s side, “passenger compartment” is an unusual way to say that in English. It sounds like what you’d call the main cabin.

On the other hand, if you have gloves that you keep in the car, at least it’s possible to keep them in that compartment.