in Windows 7's "Set up USB Controllers" windows, I confirmed the device itself is working and recognized by the OS via the Properties window's Test tab, which shows you what buttons are being held down and the tilt of the joysticks.

But Grim Fandango itself doesn't seem to recognize it at all. Is there some command line argument I need to pass?

I am also having this issue.
This was not an issue like a year ago since I was able to beat it with the DS4 native controller plugged in but now it does not recognize it.
Probably a bug or something.