The camera is important in defining what the game will be. It is how the player is able to visually see what is happening in the world. Therefore, one of the most crucial aspects of any video game. It also helps with immersion such as being able to look down and see a body in a first-person shooter. Many games follow a similar recipe in how place camera. However, there was experimentation as to how it should be handled. Especially in the early days of video games. Even going from a static frame to multiple panels in the earliest of games.
No game is a better example of this than Super Mario 64.  That was one of the first 3d platformers and had the unenviable task of introducing players how to navigate in a 3d world.  To achieve this, they made the camera a literal character in the world. By making it a character they were able to personify it. Personifying things and giving it a name, a trait makes people react far better towards things including an element in a game. Despite that it the most criticized aspect of the game in both modern and contemporary reviews. There is also a speed running exploit that is dependent on the camera. Therefore, it is taking a direct mechanical role in how game is played.
Another early game that was very influential on how the camera is perceived in the world is resident evil. It was extremely important in building the atmosphere of the game.  AS it was able to restrain the character and build tension. It was able to restrain the character as they were not able to see everything. In this restraint tension was built as it was impossible to know what was around a corner. Also, the further away you moved you physically got smaller and if the character was running towards the front of the screen they would get bigger. Although, in this case whatever was chasing the player would also grow in size thus the tension would increase.

Source: https://vimeo.com/193267720 and an in class discussion