Disconnecting my second display did not help. As I suspected, Unity is a broken POS on Mac, again. Why does anyone use them for a Mac game?! Why!? From ~/Library/Logs/Unity/Player.log:
--->InitializeDisplay()...
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
-->SortedResolutions[ 0 ] 1920x1080
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
-->SortedResolutions[ 1 ] 1280x720
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
-->SortedResolutions[ 2 ] 960x540
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
-->SortedResolutions[ 3 ] 2560x1600
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
-->SortedResolutions[ 4 ] 2048x1280
...
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->MatchResolutionToIndex(2560x1600) returning 3
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->TryChangeResolutionAndDisplayMode(3, Fullscreen)...
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->TryChangeResolutionAndDisplayMode(3, Fullscreen) _currentResolutionIndex is 3, _currentDisplayMode is Unknown
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->TryChangeResolutionAndDisplayMode(3, Fullscreen) returning false. Not initialized.
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->ChangeDisplayModeRoutine( Fullscreen, True )...
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->ChangeDisplayModeRoutine( Fullscreen, True ) _currentDisplayMode is Unknown
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
--->ChangeDisplayModeRoutine( Fullscreen, True ) calling Screen.fullscreen(true).
(Filename: /Applications/buildAgent/work/d63dfc6385190b60/artifacts/MacStandalonePlayerGenerated/UnityEngineDebug.cpp Line: 49)
Switching to 2560x1600 fullscreen
Could not find requested mode.
(Filename: Line: 104)
Switching to 2560 x1600 failed! Trying second best guess.
Switching to 1920x1440 fullscreen
Could not find requested mode.
...