Neither the Microsoft.com page, nor the Register article, mentioned Internet Explorer at all, or that would have reminded me that "Flash in Windows" really means "Flash in IE". And since I do not use, nor does my company support the use of, Internet Explorer, I've ignored (and largely lost track of) recent changes to IE. On my Windows 10 boxes I use Edge; on everything else I use Firefox, Chrome, or Opera.
So you're right, and my comment #3 at the top:
"Or perhaps someone with more time to research this can show me where the Flash vulnerabilities don’t apply to Windows 7..."was more accurate than I thought.
Thank you!
#FalseAlarm
Adobe Flash is included as a platform feature and is available out of the box for Windows 8.1, running on both IE and Internet Explorer for the desktop. Users can turn this feature on or off using the Manage Add-ons dialog box, while administrators can turn this feature on or off using the Group Policy setting, Turn off Adobe Flash in IE and prevent applications from using IE technology to instantiate Flash objects.
Important
The preinstalled version of Adobe Flash isn't supported on IE11 running on either Windows 7 with SP1 or Windows Server 2008 R2 with SP1. However, you can still download and install the separate Adobe Flash plug-in.
https://technet.microsoft.com/en-us/itpro/internet-explorer/ie11-faq/faq-for-it-pros-ie11