MV uses the OpenGL interface for display, exactly because OGL exists for different operating systems (its counterpart DirectX is windows-only). And whitescreen means that your OpenGL library is either out of date or not correctly installed, and in both cases that is a problem of your display driver.
This isn't exactly true for MV - oddly.
Both the QT run-time of the editor and the NW.js run-time of the game player use
ANGLE for WebGL compatibility, so for Windows OpenGL is not actually a requirement for MV - despite most people (including staff and developers) saying it is.
The pipeline for MV is; WebGL (as a thin wrapper of OpenGL) and then OpenGL to DirectX (OpenGL as a thicker wrapper of DirectX, thanks to ANGLE).
For a brief explanation; the OpenGL drivers on Windows are limited to GL 1.2/1.3 - and full OpenGL support is only available from your GPU vendor. Microsoft, with Windows, ships their own graphics Driver for compatibility, but this doesn't have full OpenGL support, it only has full DirectX support, so Google created ANGLE to make it so even PCs without OpenGL drivers can still have OpenGL compatibility through the expected DirectX driver on Windows.
As such, it is incorrect to say that MV requires OpenGL (or even uses OpenGL) on the Windows platform. There are exceptions to this, but if you're running the Windows version of MV on a computer then 99.999% of cases it is running on DirectX through ANGLE.
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To bring this back to the issues discussed in this thread; this means that OS emulation layers such as WINE (or PlayOnLinux) have an additional requirement for DirectX compatibility. WINE is famous for having excellent DX compatibility these days, but this means there's an extra requirement for your GPU on Linux to be able to emulate DirectX.
You're in this odd situation where your graphics API stack looks like this: WebGL -> OpenGL -> ANGLE -> DirectX -> WINE -> OpenGL and in between each of those layers are additional requirements to be able to emulate the one before it. Your OpenGL driver must support more features than WebGL, your DirectX driver must support more features than your OpenGL driver, and your OpenGL driver must support more features than your DirectX driver [hilariously]).
I'm pretty sure that MV has native Linux support now, you shouldn't be using PlayOnLinux, you're making things harder for yourself and your computer by doing so, just swap over to the real Linux client rather than jump through hoops emulating the
Nine Circles of Graphics Hell.
EDIT: for Linux the support for GLES (the OpenGL flavour that WebGL is based on) is excellent, so native Linux would be WebGL -> EGL directly (EGL being the GLES context). Isn't that far simpler than the situation on Windows? Windows EGL support is fragmented between Intel, AMD and NVIDIA (and confounded by the bad drivers, thanks to Microsoft) so you should expect better performance on native Linux.