Well, I wasn't saying that switching to GL_TRIANGLE_WHATEVER would automatically fix it. It's dependent on how your vertex data is stored/ordered after reading it from the .bsp. Also, since I haven't seen your code, I can only guess as to what your problem is based on what others have had before.
Can you elaborate on why OpenGL ES 3.0 "allows" rendering without glVertexArrays and core OpenGL 3.x DOES require glVertexArrays? As I suggested before, I recommend using indexed vertices if you haven't already. That saved me tremedous headache.