The BT Sport App on Windows 10 is now a native Windows 10 Store App and not a desktop app. It no longer uses a web browser nor silver light which is being discontinued. You should not be clicking on any link but simply open the Windows Store and install the latest version from there.
The link I posted is the one the BT website took me to when I downloaded the app, it is perfectly safe - I wouldn't post it otherwise
He definitely loaded from Microsoft site. I get the same result from the site you posted. It is the only site at Microsoft, i have not found another site anywhere.
Only other thing I can suggest is that you use System Restore to roll your PC back to a time before your first attempt to install the app and try again from scratch
I have managed to get it working by selecting the trial, i await to see if i get a message to download full version or something.