Game is running fine for me so far, just had to fix the resolution and make the camera not rotate constantly.

To set resolution and window copy ~/Games/Steam/Linux/steamapps/common/Psychonauts/DisplaySettings.ini to ~/.local/share/Psychonauts/DisplaySettings.ini and edit.

To fix the right stick on a controller making the camera rotate constantly add ~/.local/share/Psychonauts/Profiles/Profile [n]/Profile [n]- [nickname].ini and change:

LookUp_Alt=JoyRotZ
LookDown_Alt=JoyRotZ
LookLeft_Alt=JoyZ
LookRight_Alt=JoyZ

to

LookUp_Alt=JoyRotY
LookDown_Alt=JoyRotY
LookLeft_Alt=JoyRotX
LookRight_Alt=JoyRotX

I haven't really found a good button mapping for the 360 controller, as it's not seeing the analogue triggers. At the moment I'm using:

MoveForward_Alt=Up
MoveBackward_Alt=Down
MoveLeft_Alt=Left
MoveRight_Alt=Right
Jump_Alt=Joy1
Attack_Alt=Joy3
Use_Alt=Joy4
Cancel_Alt=Joy2
LockOn/Float_Alt=Joy5
PsiPower1_Alt=Joy6
PsiPower2_Alt=Joy8
PsiPower3_Alt=Joy9
InventoryMenu_Alt=DPadLeft
PsiPowersMenu_Alt=DPadRight
FirstPerson_Alt=Joy11
Journal_Alt=Joy7
Stats_Alt=DPadDown
LookUp_Alt=JoyRotY
LookDown_Alt=JoyRotY
LookLeft_Alt=JoyRotX
LookRight_Alt=JoyRotX

• https://bugzilla.icculus.org/buglist.cgi?quicksearch=psychonauts - Issue Tracker of porting company.
• https://github.com/ValveSoftware/Proton/issues/6525 - Issue for Proton version.
• https://www.gog.com/forum/psychonauts/psychopad_xbox_360_controller_gui_unofficial_patch/page1 - Patch to replace the keyboard icons in the GUI with XBox 360 controller ones, but uses an installer so I haven't tried it.