Thank you for the log. It shows that the installation of our plugin is erring out with a generic error code 3001. Thus our plugin actually failed to install to some yet to be discovered reason.
I'd like you to try manually installing it:
1) Open a command prompt window
2) Navigate to the folder "C:\Program Files (x86)\Telerik\Test Studio\TestAdapterVS2013"
3) Run this command:
C:\Program Files (x86)\Microsoft Visual Studio 12.0\Common7\IDE\VSIXInstaller.exe,Target= /u:"Telerik.TestStudio.TestAdapter.VS2013" /s:Pro /v:12.0
Does this report any error? If so what does it say?