For me "officially supported" means that MKVToolNix should run on these systems without serious limitations. I will investigate and fix bugs on those systems myself.
I will also offer binaries for those systems that I've built myself.
If an operating system or a specific version is not on the list, then MKVToolNix might still run on that system or version – but I won't spend time on fixing issues on it.
Why? There are several reasons, but the most important is that supporting systems has a cost in time. My time is limited, as is everyone else's, and this is simply where I draw the line.
Another reason may be that I lack experience developing on such a system (e.g. macOS) or lack an installation of it (again macOS, but also the various BSDs or the Solaris derivatives). Time permitting I may decide to spend time on developing fixes relating to those systems, but I cannot guarantee I will, especially as I lack systems to test those fixes on.
Supported are all client versions of Windows (meaning Intel architecture) that Microsoft offers general support for. This means Windows 10, 32-bit and 64-bit architectures. On the server side Windows Server 2012 and newer are supported.
All versions support 32-bit and 64-bit architectures except were noted.
Arch Linux (I don't offer binaries for Arch, but this is my main development platform)
I don't support macOS. I don't own a Mac, haven't used one, have never programmed in that environment and can therefore not provide support for it. I do provide binaries for it, though, and I may look into issues that are specific to that platform, but don't count on it.
As of MKVToolNix v42.0.0 the DMG only works on macOS 10.14 "Mojave" and newer.
Other systems and architectures (*BSDs, other/older Linuxes, Solaris derivatives, ARM architectures etc.)
I don't officially support other systems and architectures. This includes any type of NAS system (e.g. Synology DiskStation or QNap) and any type of Raspberry Pi and similar ones.