It's also upside down (pushing the mouse looks up)
I think you're brain is upside down. Push for up is what assume is normal.
Except on a joystick. I think of that as tilting the joystick to tilt my view. A mouse is different though, it slides on a flat plane. I sort of assumed most people were like that with a mouse. I don't think I've ever installed a FPS that had pushing the mouse make you look down.
It's cool to see them ported to flash like this, though it feels a bit odd. I noticed once my mouse got to the edge of my screen (even though I was holding the left button), I couldn't look further in that direction. I recently got Doom and all working on Doomsday too. I have multiple copies of Doom. I think I have the original CDs for Doom and Doom 2 (probably a re-release, as I think thet were originally only released on floppy), as well as the collector's edition pack. I also bought Doom on XBLA, and it plays fantastic with the controller. (I don't like using a mouse with Doom. Mouselook wasn't originally in, and it throws me off to have moving forward/backward on the mouse, or even having nothing on the mouse Y axis throws me off.)