Can't open web project because IIS Express is not installed (even though it is)

The way I found to make it work was by looking for the <ProjectExtensions/> tag and replacing it with:

  <ProjectExtensions>
    <VisualStudio>
      <FlavorProperties GUID="{349c5851-65df-11da-9384-00065b846f21}">
        <WebProjectProperties>
          <UseCustomServer>True</UseCustomServer>
        </WebProjectProperties>
      </FlavorProperties>
    </VisualStudio>
  </ProjectExtensions>

In the absence of a request for a suitable web server in the csproj file, it defaults to its own best guess, which in this case happens to be IIS Express. So in this case, the answer was to change the UseIIS option to True, and the project opened correctly.

<UseIIS>True</UseIIS>