I have tried multiple joysticks (Atari CX-40+, original Atari CX-40, Epyx 500XJ) with the same results. I have a Commodore 64 Ultimate.
I assume the problem is on my end. I do not have problems with any other games with joystick directions.
When I have time, I will see how to reset the C64U back to the default configuration since I doubt other C64U owners are having this problem with your game.