Resident Evil 4
Resident Evil 4 is a survival horror game, but it's also a shooter. By that I mean, compared to the games before it, Resident Evil 4 actually embraced shooter-style mechanics like free-aiming.
This game broke the dam on third-person shooting action in AAA games. After Resident Evil 4, shooting games started to try mimicking its style both inside and outside of the horror genre. You could argue that Resident Evil 4 is responsible for blockbusters like Gears of War. The connective tissue is there.