Why do I need to inverse the orientation matrix of a camera to be able to translate it in the direction it is facing?
People always forget that there is no "camera" in OpenGL. In order to simulate a camera you have to move the whole world inversely. So if you want ur camera looking 30 degrees downward, you move the whole world 30 degrees upwards. If you want your camera moved to the left, you move the whole world right. That's why you will notice the "-" sign in the translation vector where he used the variable position. 

Hence the reason there is no separate "view" matrix in openGL, it's modelview matrix combined. That's the reason for taking the inverse. Since a view matrix represent's the camera's forward, up and side, you have to take the inverse since the orientation is defined for the world not the camera.