I think you're ignoring how small the definition of "game" truly is. For example, you need exactly none of the things you just described you make Flappy Birds.

I think you're ignoring how small the definition of "game" truly is. For example, you need exactly none of the things you just described you make Flappy Birds. Hell, insisting that a game engine isn't a "real" engine unless it can render 3D graphics on a GPU ignores such a huge swatch of games it's hard to know where to even start.