Game Banished and others do not start (failed DLL_PROCESS_ATTACH for VBoxOGL.dll)

VBox 4.3.6, r62281.

The recently released indie village builder Banished cannot be started (error is slightly different with Guest Additions installed), this message box appears:

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A fatal error has occured and the application cannot continue.

VideoDevice: Failed to initialize a video interface. The renderer DLL isn't loaded or isn't supported on the OS.
VideoDX9: The application failed to create a DirectX9 interface.
VideoDevice: Failed to load or initialize a video interface!
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No change even with directx_aug2009_redist.exe installed. Debug log with both missing and installed Guest Additions is attached.