"CONTROLLER SUPPORT" TAG
Please double-check if "Controller Support" tag is present on the game's store page. Some of our older games might indeed had controller support in the past, but might no longer be supported with modern systems.
DISABLE STEAM FROM RUNNING AT STARTUP
Quite often Steam controller support is interfering with the game. Closing Steam does not always resolves the issue. In that case, please disable Steam from automatically starting when your computer is booting. In order to do that simply start Steam, click on Steam menu, and choose Settings. In the Settings window, switch to Interface tab and disable "Run Steam when my computer starts".
TRY EMULATING KEYBOARD/MOUSE ACTIONS ON YOUR CONTROLLER
In some circumstances your best option is to emulate keyboard and mouse movements on controller using software like Enjoyable:
This guide, by thefluffyfist, could be helpful: