TypeScript is probably not installed on your build server. To install it, copy your TypeScript folder from c:\Program Files (x86)\MSBuild\Microsoft\VisualStudio\v12.0\ to the same folder on your build server (where v12 is the version of your Visual Studio).
The Visual Studio version on your build server can be different however. In my situation, the version on my development machine is v12, while the build server uses v11. I found that out by adding the following to the [WebProjectName].csproj file:
<Target Name="PrintVisualStudioInfo">
<Message Text="VisualStudioVersion: '$(VisualStudioVersion)'" Importance="High" />
</Target>
<PropertyGroup>
<CompileDependsOn>
PrintVisualStudioInfo;
$(CompileDependsOn)
</CompileDependsOn>
</PropertyGroup>
Be sure you put it after the last <Import /> element. Now when you look at the output of your build on the build server, you should see 'VisualStudioVersion: xx' somewhere.
Copy the TypeScript folder to the correct version folder on the build server.