There was a real danger for a few years in the mid-'90s that competition between browsers would manifest itself in a proliferation of proprietary tags that only worked with one browser or another. The old "Best viewed with..." buttons that sites used to festoon themselves with (examples: http://cjihrig.com/blog/wp-content/uploads/2011/12/best_view...) were an artifact of this; they advertised that a site used one browser or another's particular set of proprietary tags, which was how you positioned yourself as "cutting edge" in, say, 1996.
Things are better now, thankfully. (Not much better, but better.)
"Google Inboxbeta only works in Chrome"
I’d say things are just as bad as before
Chrome has become the new IE in the meaning that it supports weird special stuff, but sometimes not the official W3C definition, and webapps rarely work on multiple browsers.
You know that venture giant, the 'A' in A16Z? Long time ago he was marca without the initial 'p', maintained an emacs clone called Epoch, and also hacked away on a web browser called Mosaic:
http://1997.webhistory.org/www.lists/www-talk.1993q1/0182.ht...
Probably invented by some lunatic.