Obviously we should take Wikipedia with a grain of salt, but here's their definition of Survival Horror -
Survival horror is a
subgenre of
video games inspired by
horror fiction that focuses on survival of the character as the game tries to frighten players with either horror graphics or scary ambience. Although combat can be part of the gameplay, the player is made to feel less in control than in typical action games through limited ammunition, health, speed and vision, or through various obstructions of the player's interaction with the
game mechanics. The player is also challenged to find items that unlock the path to new areas and solve puzzles to proceed in the game. Games make use of strong horror themes, like dark maze-like environments and
unexpected attacks from enemies.
Now, let's use this when talking about RE4.
1.
focuses on survival of the character as the game tries to frighten players with either horror graphics or scary ambience. - RE4 definitely does this. Far more than RE5 does in terms of ambiance. Through nearly the entire game, we're in a setting that, were it real life, would inspire fear.
2.
Although combat can be part of the gameplay, the player is made to feel less in control than in typical action games through limited ammunition, health, speed and vision, or through various obstructions of the player's interaction with the game mechanics - Now, here RE4 is less Survival Horror than its predecessors, however, I feel it still fits. Not being able to move when you shoot, no cover system, Quick Time events. I'd also argue that movement speed is slow compared to most action games, and you do lose healthy easily/quickly. So all in all, while it doesn't do these things perfectly, it still hits the mark for survival horror.
3.
The player is also challenged to find items that unlock the path to new areas and solve puzzles to proceed in the game. Games make use of strong horror themes, like dark maze-like environments and unexpected attacks from enemies. - RE4 doesn't have many puzzles, but they are there. Most are pretty lame and consist of just shooting stuff, but every now and again you have puzzles like Ashley moving around the squares to make a design, or Leon finding the right number of bodies in group of paintings. Puzzles are RE4's weakest point in my opinion, but they are there, and obstruction of moving forward is pretty common in RE4 as well.
All in all, while it falls short in some areas, I'd say we can definitely say it IS Survival Horror. Now, that doesn't mean it deserves all the defense it gets. But you started this off saying it wasn't even survival horror, and I'd have to disagree with that initial statement.