On tablets, YouTube will serve H.264 files, hence why it works on iOS and Chrome on Android 4.1.

On the desktop, they will block the HTML 5 player which serves H.264 or WebM if the video has ads enabled. This is a preference the uploader has, to generate revenue off the playback. The uploader can also block mobile (phones/tablets), or embeds if they want, as those environments may not have ads.

For a while they outright lied and said "This video is unavailable". Now they have been saying Flash is required.

I got tired of the song and dance of their HTML 5 perpetual beta, and instead installed the Youtube5 extension (http://www.verticalforest.com/youtube5-extension/). Their player tends to also just work better then the Google HTML 5 one.

It's rumored that the iOS YouTube app went away because the existing contract ran out, and Google would only renew if Apple allowed ads in.