This site is about long distance trails--things that take weeks or months to complete, not stuff like your Old Rag for which every listed hike is in day-hike range. I don't see trail distances on your second link but once again it appears to be day-hiking.
Considering the US ones on that list--there are people that have managed to do all three in one year, albeit with some flip-flopping. There are more of them than there are moonwalkers.....still living.
It's not about standards, it's about off topic. The trails you are referring to are far enough from me I know nothing of them, they very well might be good trails. They aren't long distance trails, though.
Old Rag Mountain (Shenadoah, VA) https://home.nps.gov/places/old-rag.htm
and
The Mohonk Labrynth Trail (Catskills, NY.. so much fun hiking in caves, up ladders, etc) https://www.mohonk.com/a-day-at-mohonk/hiking/