The WIN 7 screenshot shows that the app is using ActiveX print mode.
The WIN 10 screenshot shows the app using pdf print mode.
I have actually not used WIN 10 with an app that uses ActiveX print mode, but from what you are describing I am rather surprised at the behavior. I'd suspect some warning / error re use of ActiveX on WIN 10. See:
Microsoft Removes ActiveX In Windows 10 Default Browser Edge : PERSONAL TECH : Tech Times
Windows 10 - ActiveX on Internet Explorer 
The following may be your way out:
Adjust Internet Explorer ActiveX settings - Windows Help
- Ludek
Senior Support Engineer AGS Product Support, Global Support Center Canada
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