I wonder if that's not by design in order to reduce the effectiveness of spamming. Are links to pages within chess.com also not live? I know this is how it used to work in live chess.
If so, I'd suggest that with the in-game chat box efforts to reduce the effectiveness of spamming in this way are somewhat redundant with the disable chat option and there's little risk in enabling all links.
When (or if) in-game chat gets a makeover, it would be useful if URLs within the chat box were live so that clicking on them opened a browser window.
Currently it is necessary to copy & paste a link into a browser window, and I for one, am plumb exhausted after such sub-optimal dragging & clicking.