mostly the game will support a controller but the shoulder buttons wont work. and the buttons that dont work on a controller actually have controls on the keyboard. is there any game manual of guide that lists the games pc controls?
the ones i seem to have found so far...
wasd usually is the directional controls
C is menu
X is back
Z is confirm
Q & E seem to be shoulder buttons
thats all ive been able to find out so far...

When you open up the game, the GOG Configuration window has an Input tab that you can use to rebind the controls.

I'll agree that the defaults feel kind of strange. I think that the intention was to allow the arrow keys with ZXCV, and the option to use WASD with similar controls elsewhere on the keyboard. I still found it better to just rebind controls into something more sensible, although it might be hard if you aren't already familiar with the game controls to begin with.