I just tested this in Chrome on Android and it's not true; I'm able to browse Quora all I want without downloading any app (although there is a prominent button that says "View in Quora App").
To be really sure I also tested it in Safari on iOS and the experience is the same.
To be really sure I also tested it in Safari on iOS and the experience is the same.
I can post pictures if you don't believe me! ;-)