Seeing as I don't have a problem when I go to YouTube to watch the videos I am going to lay the blame with the developer of the platform that this forum uses.
Apple is part of the group that sets the standards, they are not the problem.
I would guess that this site knows that mobile Safari does not support Flash and defaults to HTML5. The could conversely be wrongly assuming that Safari for OS X all have Flash but that would be silly as Apple has not shipped it installed for years.
Judging by the quality of the AutoGuide app I think I can guess where the issue is.
I get the error on lots of sites. Apple knows this,. They know about lots of bugs they dont fix. Perhaps youre also right about the defaults, but this site is not alone with the problem.
When you install the CLICK TO FLASH plug in (that apple features on its front page btw https://extensions.apple.com
), safari now reports NO FLASH HERE, and the site now provides HTML5 instead.
That Youtube has decided to work around and fix apple's bug is kudos to them. In the mean time, with safari, you'll have this problem on many sites.