Very good question, FPU!
It's not impossible with one mouse, it's just that it won't result in an authentic 2 player calibration. True, changing ports won't work, but you can ID both guns to one mouse by editing the INI. For me, this works by having RawDevP1 and P2 both set as 0, as opposed to having a separate ID for each gun as shown in the video. This way, one mouse controls both guns, allowing for successful, if improper, completion of calibration. If you're only going to do single player, though, then this kind of configuration method is still perfectly acceptable; you just won't ever be able to play a proper 2 player game that way.
This is what I've done:
UseRawInput=1 ;Read mouse through Rawinput, allowing 2 mice
RawDevP1=0 ;Assign specific RawInput devices to players. If you have more than 2 mice
RawDevP2=0 ;set which one is assigned to each player (0-based)
However it's still unable to register gun calibration for player 2.