But why should you limit yourself?
Because Specialisation is the name of the game. Jack of All Trades, Master of None.
You can learn to appreciate other trades and how they affect your main specialisation, but we aren't living the Renaissance any more and nobody is like Leonardo Da Vinci. It's beyond critical to have a focus and be DAMN good at that focus so you stand out and can get somewhere in your prospective industry.
Graphic Design is well appreciated by the other two, but it's so rare for Games and Movies to see eye-to-eye, and video games already have about a million positions that are also highly specialised. I would absolutely
not recommend anybody to go a games course, but instead take a course in which ever pathway you desire most (like a Programming or Graphic Design course).