I confirm, solid as a rock, run as on Windows and perhaps better ;)

The game crashes for me on the screen with "Press A / OK Key" after the logo when my 360 Controller is plugged in. Runs fine if I remove the gamepad or skip the logo by hitting escape.

Specs:
Ubuntu 18.04.1 LTS
GeForce GTX 1060 (396.51)
Proton 3.7

Don't have a crash but I can confirm that the x360 controller is not working.

I can not reproduce your issues with Machinarium and a x360 gamepad on Ubuntu 18.04, works very well here.
I'm using the 396.54 Nvidia drivers.

Sorry for the noise. Tested again and it works just fine.

Whitelist Request

• Name of the game to be whitelisted: Machinarium
• Steam AppID of the game: 40700

System Information

• GPU: Intel Corporation UHD Graphics 620
• Driver/LLVM version: Mesa 18.2
• Kernel version: 4.18.3
• Link to full system information report as Gist
• Proton version: 3.7-6

I confirm:

• [x] that pressing the Play button in the Steam client is sufficient.
• [ ] that runtime config options
  are necessary to run the game.
• [ ] that no workarounds other than the mentioned ones are necessary.

Issues

• [x] I haven't experienced any issues.
• [ ] There are no issues left open for this game.
• [ ] Although I consider the gaming experience equal to Windows there are
  remaining issues:

This game only shows black screen and does not support ultrawide resolutions unsure of 4K resolution. Is there a way to force it into windowed mode?