Your controller isn't being detected and only keyboard keys are being detected.

For whatever reason this game only will accept controls from the first controller it picks up.

In my case both Steam and Windows was seeing a 2nd generic game controller even thought I don't have one plugged in at all. You can check this in Steam Big Picture mode's controller settings and looking to see if it shows multiple devices at the bottom of the screen and/or in Windows via the start menu by typing in "set up usb game controllers" and seeing if it shows more than one controller.

If either of these are showing unexpected controllers (such as 2 axis 8 buttons, like in my case) then do the following:

• Click the Windows Start Button or press the Windows key on your keyboard.
  
• Type in device manager and click it to open it.
  
• Click the drop down arrow by Human Interface Devices and look for a device called HID-compliant game controller.
  
• Right-click HID-compliant game controller and select disabled device.

The game should now detect your controller. This shouldn't have any impact to anything else, in theory, but if it does you just have to go back to device manager, right-click the device again, and enable it.

If for some reason this doesn't work for you, your other option is to manually map keyboard keys to your controller via Steam's controller configuration aka Steam Input, but this won't be ideal because your joystick will essentially be mapped to 4 directions versus the precision/freedom an analogue stick offers. I'd suggest trying to find/unplug/uninstall whatever else may be being detected as a controller instead.