I have finally sorted that out. I had to debug the runner as described here - https://github.com/machine/machine.specifications/blob/master/debugging-resharper.txt. And I found out that the runner was built for ReSharper 6.1.37.86, which is not the latest 6.1 release, list is here - http://resharper-support.jetbrains.com/entries/21206508-Where-can-I-download-an-old-previous-ReSharper-version-. The latest 6.1 release is 6.1.1000.82 which is installed on my machine. So the runner just could not find required ReSharper assemblies during startup. I fixed the problem by adding assembly redirects into devenv's config file. The redirects are needed for all ReSharper files the runner depends upon, there are 16 of them in total. Example redirect is:
<dependentAssembly>
<assemblyIdentity name="JetBrains.Platform.ReSharper.ComponentModel" publicKeyToken="1010a0d8d6380325" culture="neutral"/>
<bindingRedirect oldVersion="6.1.37.86" newVersion="6.1.1000.82"/>
</dependentAssembly>