|Ta-da! Amazing fullscreen! /sarcasm|
Read on after the break for the entire scoop and to see a solution.
I have always maintained that the YouTube built-in app is really bad and I have even taught you how to open all YouTube links in Safari on the constantly updated YouTube web app. But it looks like the online video player is moving to the trash can as well.
The new YouTube player looks a lot like the desktop player. But it has bigger controls and is better suited to touch screens. It also allows you to select quality more like the desktop player (360p, 480p, 720p etc. instead of HQ on and off).
However, since this player is built in HTML5, videos don't play through the regular iOS player. Therefore, tapping the fullscreen button or pinching outwards will not do what you expect. The video player now fills the web page area in Safari rather than going true fullscreen. The HTML5 player on desktops had this behavior once as well, until a workaround was put into place. But unfortunately, given how iOS works now, Google will not be able to bypass everything and make its videos go fullscreen in this player.
Currently, there doesn't seem to be an opt-out available anywhere.
One solution is to use the built-in YouTube app. However, it doesn't play in low quality (which sucks for slow connections).
There is another workaround. You can scroll to the bottom of the web app and tap Desktop to go to the regular desktop YouTube. That website still plays in the regular player (as of now), but you may encounter a few problems here and there. Some videos may say "This video is not available on this device" while they play on the mobile version (weird). However, this way to play YouTube videos not available on mobile devices still works generally (weirder). Some videos may play in the desktop HTML5 player at times and there doesn't seem to be a workaround for that (or try clearing your cache).
Otherwise, you can wait for the standalone YouTube app that Google will release once iOS 6 is out.