The issue: The game relaunches itself right after exiting or quitting it. This is an issue that also happens on Windows XP all the way up to Windows 8.
The fix: There are several tips from other users to be found via the official forums:
Launch, play and quit the game in windowed mode.
Running the game as admin fixed the issue for me on Windows, but Wine already runs with admin-rights at default. Try launching the ACM.exe in Windows98 mode and see how that goes.
Verify your games cache via Steam.
Enhale fur from a squirrel.
This issue has been discussed several times on the official Steam forum. Feel free to join the forgotten souls:
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