Well, LICEcap is open-source, so you could check for yourself.
BTW, I only glanced through the linked discussion, but I think it's about UWP apps, so I'm not sure if what LICEcap does even applies.
I tried looking through the code but couldn't track down where it gets this info. And when I was talking about "newer windows apps" UWP is what I meant.
I think LICEcap uses BitBlt() to "cpature" (copy) screen data, see line 1203 in licecap_ui.cpp. It looks like it gets its DC via GetDesktopWindow(), which is why I suspect this might not work in UWP apps.