VSCode is not open-source, and neither is this extension.
Much F/OSS on Windows and virtually all F/OSS on macOS has proprietary build dependencies (e.g., MSVC on Windows, Xcode and various Apple frameworks and GUI toolkits on macOS), but is still itself F/OSS. It's true that such software doesn't promote or embody software freedom to the same extent as free software written for free platforms and built with free toolchains and dependencies.
But this case isn't about that. Reread the comment of maintainer (presumably an MS employee) at the end:
> I'm sorry to let you know that our license also prohibits using our extension in alternate distributions of VS Code - only the official one produced by Microsoft may be used. So even if we did produce a RISC-V version, you wouldn't be licensed to use it with Code Server.
That's just proprietary, software plain and simple.
Recall freedom 0 of the free software definition:
> The freedom to run the program as you wish, for any purpose (freedom 0).
In the way that third-party distributions of VSCode do not come with the same rights to extend the software or use it in combination with compatible extensions as the first-party distribution does, VSCode also fails the test of freedom 3, regardless of the license of much of the code:
> The freedom to distribute copies of your modified versions to others (freedom 3). By doing this you can give the whole community a chance to benefit from your changes. Access to the source code is a precondition for this.
It's not that your modified copies must give your users the same rights to inspect and modify the code as you had (that's copyleft) but that you are unable to give them such rights. MS does this not entirely through the licensing of VSCode but also through the licensing of certain extensions, but the actual outcome is the same.
It's not a different story for the term open-source. This:
> May we ask why you'd like to do this? If you're planning to redistribute the language server binaries as your own custom offering, please note that our runtime license prohibits that.
means that the extension fails condition 1 (the redistribution criterion) of the open-source definition. And VSCode not allowing modified redistributions the same rights as the original fails condition 3 (the derived works criterion).
Neither VSCode nor this extension is open-source. They're both just proprietary software with some open-source components.
Free Software Definition: https://www.gnu.org/philosophy/free-sw.html.en#four-freedoms
Open-Source Definition: https://opensource.org/osd
Note that these are not definitions in the ordinary lexographical sense. They are terms that were created with explicit social and technical purposes in mind, by and for organized movements. This isn't an argument from the dictionary but a reminder of the purposes of these concepts.