2) You can't actually use an xbox controller with a computer (and hence with firefox) anyway without a USB cable. You could use a 360 controller, but not the first Xbox.
Xbox 1 controllers are just USB. You only need an adapter. Microsoft made them for a while for Final Fantasy. If you just cut the end off a controller and a usb cable, the wires inside are even properly color-coded.
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1) It's a general joystick api, not just xbox.
2) You can't actually use an xbox controller with a computer (and hence with firefox) anyway without a USB cable. You could use a 360 controller, but not the first Xbox.
Xbox 1 controllers are just USB. You only need an adapter. Microsoft made them for a while for Final Fantasy. If you just cut the end off a controller and a usb cable, the wires inside are even properly color-coded.
I'm fairly sure you need a separate driver for controllers from the original xbox (http://www.redcl0ud.com/xbcd.html)
USB xbox 360 controllers don't need any installation last I checked.
A quick Google reveals drivers for Windows, as well as drivers for Linux and Mac OS X. I feel it's safe to say that drivers are needed for either.