Earlier quoted context omitted.
Screenspace was always x-right, y-down (aka Cartesian quadrant IV) because that was the convention NTSC used to paint the screen. 3D has not had the benefit of an obvious hardware model to emulate. Y-up, Z-up, Y-down are probably the three most common variants though.
Who else in 3D uses Y-down? I’ve seen Y-up / Z-into-screen (a la Direct3D), Y-up / Z-out-of-screen (a la OpenGL convention), and Y-into-screen / Z-up (top down type games like RPGs, RTS etc.) I haven't seen Y-down (in 3D space) since software rendering days. I've yet to meet the monster who would use X-left. :P
It's all arbitrary anyway, so why not let one thing be consistent instead of saying "Y is down on the screen, but in the world Y is sideways and Z is up."
(I do still think it's weird, but I'm sure I'd get used to it)