In graphics programming, we don't use such terms arbitrarily. Mono=1, plain and simple.

The original Macintosh was proper monochrome, either pixel on or pixel off, a true 'binary image' as your definition states.

You ever try reading or writing graphics software? Nowhere in our code will you ever see anything besides 1 bit per pixel referred to as monochrome.

What the GameBoy has is 2 bits per pixel, which means its a paletted image, and looking past the puke green color of the screen, is otherwise considered a crude form of greyscale, not monochrome.