The meat of this question is below. Note that he asks what if they DON'T have those browsers installed.
I read somewhere that you need either firefox 11 or chrome 18. But what if players don't have those installed.
If they don't have Firefox or Chrome (Versions that support GamePad) then they need to update or install them. IE and other browsers do not yet support the GamePad API. I had a talk with Microsoft last week and was told currently they have no plans for the GamePad API as touch is a bigger priority for them currently.
So you are stuck with GamePad API only working in FireFox or Chrome. If your users won't have those, they will have to use keyboard/Mouse or Touchscreen.
The other option is hope that someone like ludei or appmobi or phonegap comes up with some type of way to expose the OS GamePad support to your game, or find a library that can be used to add GamePad support if there are any out there.