What app is that? Try to run that in the Compatibility Mode. Go the properties of the Application Executable - Go to Compatibility tab and set that to run in Legacy Mode. For Eg, Set that to Windows 7 and see if that runs.
What's the App to do Job? In which code is it written? Has that ever worked? If yes than on which Operating System?
I would agree "some" apps. I have two Windows 10 computers here: one with a Microsoft Account and one with a local account. Most apps work under both methods.
Thank you for the update and I was happy to help you with this.
Windows OS
This topic area includes legacy versions of Windows prior to Windows 2000: Windows 3/3.1, Windows 95 and Windows 98, plus any other Windows-related versions including Windows Mobile.
Try SFC /Scannow then Retest.
Create a new User account with Admin Rights, switch into that and retest,