we don't really have a way to handle this if you don't have the privilege to write in the directory on non-windows platforms, we can look at extending the test framework for next release.

I recommend a test hook approach, which allows you to provide an alternative location. From a test perspective, the only thing you want to be sure of is when you select a location the files get placed there. It doesn't really matter what that location is, it could be anywhere - A testhook which makes [system.management.automation.platform]::SelectProductNameForDirectory('SHARED_MODULES') point to $TESTDRIVE should be sufficient as long as you have a separate test which returns what the default location of SHARED_MODULES should be.
This provides far more flexibility in the long run
If you can't do that, I would mark this specific test as pending for non-windows

Please use -Pending instead of -Skip. We track all pending tests because they are supposed to work but now at the time. -Skip means they are not applicable to the platform.

And also, please add -Pending before the open curly bracket, like

It "Should install a module correctly to the required location with default AllUsers scope" -Pending:$IsLinux {

Same comment here.