Thank you for getting back to me.
I double checked the provided link and it is really for Team Explorer 2017 which unfortunately does not deploy the required dlls as Team Explorer 2013 installation would.
Since the issue is known for us we've been working on resolving it. The workaround we previously provided was the mentioned installation. Though the download links for Team Explorer 2012 and 2013 were recently deprecated from Microsoft so the priority of that task was raised. We possibly have identified a fix which is not yet live in Test Studio version but is expected to be published with our next Service pack release.
Though we researched for another workaround until that next version comes live and here it is.
1. Please download the Microsoft.Mshtml.dll from this location
and store it to C:\temp folder.
2. Then Run PowerShell as Administrator (PowerShell is automatically deployed with Windows 10)
3 .Run the attached script.
For your convenience I have saved the script in a txt format and attached it zipped. You could either copy and paste the script text to the PowerShell console or save it as a Windows PowerShell file format (*.ps1 or *.psm1) and run it. Please note that the script searches the dll file in C:\temp.
The script will register the previously downloaded dll in GAC and will be available to be used by Test Studio which should solve the issue you are facing with IE recording and execution.
Please let me know if you would need any further assistance. Thank you in advance for your cooperation!