Shooting was an ancillary mechanic. The majority of the early Resident Evil games were spent exploring and solving puzzles, while the best response to most enemies was simply to go around them.

A shooter implies shooting is the primary gameplay mechanic. Hitman 2 has a bunch of gun, and you can shoot people with them, but it's not a shooter because you spend the vast majority of the game not actually shooting people, and when you do it's often not even the best solution.

The original Resident Evil 1, 2, 3, Zero and Code: Veronica are horror games. They might have guns, but that doesn't make them shooters. If they were shooters they'd have made the shooting mechanics less atrocious in the five different original releases and the one remake they did that all use basically the same clunky mechanics.