Do you need OpenGL to develop a game?
In order to develop a game, you need a way to communicate with the GPU. This is where OpenGL comes into play. OpenGL is an API that allows you to transmit data from the CPU to the GPU. The data that you normally send to the GPU are the vertices, normals, UV coordinates of a mesh. A mesh could be a game character.
OpenGL is language independent, so you can interact with the API by using programming languages like C, C++, Objective-C, etc.
So, in order to develop a game you need to have access to the GPU. You get access to the GPU by using the OpenGL API. You interact with the API with the languages mentioned above.