Shadow of the Colossus was an extremely ambitious game at the time. Not just for how it portrayed an open world but also how there are no enemies in the game, at all. It's focused entirely on it's 16 boss fights, one after another that are all extremely distinctive.
There's several that require the player's horse in order to even get close to. There's a few which you cannot climb directly but must climb an adjacent temple in order to jump onto. There's one that flies.
and a few that are eel like and swim underwater
Hell the 13th colossus doesn't even attack the player.
So I don't see why they're "all fought the same way". Just the sheer scale of it's boss fights still remain largely unparalleled. Only games like the Witcher 2 even came close and even there it wasn't as focused upon.
The game also has very subtle sidequests. There are lizards around the world either at save points or just on random buildings the player can kill with their sword. Doing so increases your grip gauge. While this is all well and good it allows you to climb some fairly large landmarks that are impossible to traverse without. This is including the temple the player starts the game at, you can climb up the entire thing and find a secret garden the developers mapped out for players to find.
SotC is almost more of an elaborate puzzle game than an action game. The action elements are heavily muted, and it's focus on minimalist storytelling is paramount.
https://youtube.com/watch?v=S1T-f3dIUZE