I'm not exactly sure when it started happening, but with modern versions of Windows, it seems some parts that aren't games are controllable with a gamepad, such as the Start menu. I don't care for this behavior, or any other means of controlling my computer's boring functions via gamepad, so I went searching online for a solution.
User danVnest over on SuperUser.com gives us a solution. In case that link becomes inaccessible, here's the Windows Registry change that should apply the fix:
Windows Registry Editor Version 5.00
If you copy and paste the content of that box into a file with the .reg extension, you can then double-click on it to apply the registry tweak. The changes may either require signing out and back in, or rebooting the system.