Actually, no, you do not need a darkroom to develop film. The film is extremely light sensitive and requires total darkness at certain points in the darkroom process, like when transferring the film in the film development tank for chemical processing. However, this task can be done without a darkroom, in a film-changing bag, which is light-sealed to protect the film. Film-developing tanks are also light-sealed so that you can pour chemicals in and out without having to expose the film to light. Once the film is fully processed, it is no longer light-sensitive and safe to remove from the tank.
You will need a photography darkroom when making prints of your images with a negative enlarger. Enlargers require enough room for developing photos. You'll also need basic darkroom equipment to chemically process those prints, especially if they are large in size.