Chrome could have 100% market share and it wouldn't necessarily be a problem. If I understand it correctly, Google would have to abuse their market position in some way.
Various other sites can get added to the whitelist if their videos are big enough and the user plays them often enough. But YouTube starts out on the whitelist. It's possible that dailymotion does too. The BBC, doesn't seem to be on the whitelist, though.
You knowblike Google do if you access any of there services not in chrome "download chrome here", "this site works best in chrome".