With respect, the archived flash player document said it would no longer do older versions than 11.0.
Adobe saying that they no longer support older versions does not mean that you can not download them and use them.
How can I re-install Adobe Flash Player 10.1? Don't know how I lost it but my system will not support 11. Thanks!!
Installing an older version exposes your system to attack as described in this Adobe security advisory: http://blogs.adobe.com/psirt/2011/09/security-update-available-for-adobe-flash-player-apsb 11-26.html
If all you want to do is watch videos on Youtube, you don't need Flash and can watch them in HTML5 instead. All you need to do is to install Firefox which supports WebM. Firefox will run on most systems without a problem: http://www.mozilla.org/en-US/firefox/8.0/system-requirements/ (download link on the same page).
After you install it, go to this site and click the link at the bottom called "Join the HTML5 Trial": http://www.youtube.com/html5