To fit in the one button theme, I added that it blocks input when more than one key/mouse button is pressed at once. The game renders with colors onto framebuffer. Postprocessing shader converts the colors into grayscale (brightness between 0 and 1) and adds random number (also 0-1) to it (which just is hashed position). If the result is greater than 1, it sets color to white. This is a simple to implement dither-like effect. You can try to play with it - shaders are compiled at runtime, so you can change them in data/shaders/post.vert and data/shaders/post.frag. There is also edge detection function, which was my second idea how to make the game 1-bit, but it didn't look that good, but I kept it there anyways.
Looking at your game screeshots (sadly I can't play it; the build is 64-bit, but I'm on 32-bit windows), it seems like you used real dithering. May I ask, how is it done? :P