I checked and something is look different in your Video. When I right click on Outlook I get this menu.

Which is, I believe is the correct one to be pinned. Not really sure why in your video it come as "Microsoft.OutlookforWindows". And, I checked deeper, its the way you pinned to taskbar while launching outlook via Windows 7/Modern style Start menu. And yes, I believe, this is related to that other issue you mentioned in your reply#2 on pinned item on Start panel. So, I have forward your problem to Stardock Support Team for their review. Please keep an eye on this thread for any updates. We appreciate your feedback and patience.
As a work around please change to any other Start11 style other than Windows 7/Modern style and Open up Outlook from there. Than pinned to taskbar while Outlook is open.
Thank you,
Basj,
Stardock Community Assistant