This specific joystick model does not use Rx and Ry, which makes proton naively forward Rz as Rx and U as Ry (as it works purely off axis index). For some games that recognise the joystick, this means they will try to read the wrong axis and ignore the active ones.
This is the case for Nuclear Option, which uses Rewired for input handling. I suspect it could be the case for all games that use this library.

I made a local fix to be able to properly play, and I figured I could at least try to share it in case it helps other people too