But the mouse is not inverted.
However if you wish to play with inverted mouse, I believe there's a number of mouse inverter programs out there. I found this one, for example: https://superuser.com/questions/406502/how-can-i-reverse-mouse-movement-x-y-axis-system-wide-win-7-x64
EDIT: Sorry to say, I tried it and it only works on the desktop. Guess you'll have to keep googling for a solution. Presumably there's even a global setting for some Unity game config file to invert mouse controls.