There are 2 video codecs for HTML5 videos available --- h.264 (which the Playbook supports) and webm (which the Playbook doesn't support).
If youtube has a video encoded in h.264 --- they can stream it to you via flash or HTML5. If youtube has a video encoded in webm for HTML5 --- then the Playbook cannot play that video.
Your 2nd screenshot specifically tells you that the Playbook doesn't support webm html5 video. The video in your 1st screenshot is a webm encoded video --- you can verify that by youtube's advanced search filter and search only for webm videos.
If you use the Opera browser on a PC --- the reverse happens. Opera supports webm HTML5 videos but doesn't support h.264 HTML5 videos.
You won't see webm html5 videos being supported in handsets/tablets for at least a couple of years --- because the chipsets currently on market has only h.264 hardware accelerated decode. RIM can't do webm on the Playbook even if they want to do it --- because it is not hardware accelerated in silicon.
Also search this webm video
WebM Demo with Leonardo Dicaprio - Shot with Red Camera
This video plays on my blackberry phone and Playbook
Going through the full desktop version not
The mobile app.