Two years after the question was asked, using Visual Studio Command Prompt still did not produce right answer for me. But the usual Help|About window seems working these days:

UPDATE (June 2017):

1. VS 2013 does NOT show this info. (Later note: VS 2017 Enterprise edition does not show this info either).

2. VS uses Microsoft Build Engine (MSBuild) to compile Typescript files. MSBuild can support several major releases of Typescript, but About window shows only the latest one.

Here is how to get to the bottom of it:

A. To check which versions of Typescript are installed with your Visual Studio/MSBuild, inspect contents of C:\Program Files (x86)\Microsoft SDKs\TypeScript folder. For example, I have versions 1.0, 1.8 and 2.2:

B. Check which version of Typescript is requested by your project. In *.csproj file, look for <TypeScriptToolsVersion> tag, or you can add it if it is missing, like this

    <PropertyGroup> 
        ...
        <TypeScriptToolsVersion>1.8</TypeScriptToolsVersion>
        ...
    </PropertyGroup>

C. Finally, you can check, which version of Typescript is actually used by MSBuild. In TOOLS | Options | Projects and Solutions | Build and Run set MSBuild project output verbosity to Detailed:

Then build your project and inspect the output: you should see the reference to one of Typescript folders described in (A).