Latest news is that YouTube is switching to HTML5 as the default format:http://arstechnica.com/gadgets/2015/01/youtube-declares-html5-video-ready-for-primetime-makes-it-default/, http://youtube-eng.blogspot.com/2015/01/youtube-now-defaults-to-html5_27.html. You should soon be able to play videos sans Flash.
For historical purposes (and in the event that YouTube reverts to Flash), here is what I'd noted previously:
Since YouTube has changed video formats, apparently in an effort to restrict downloading, there is currently no way to view the video in "real time" without using Flash AFAIK. "Real time" or "live" viewing is a misnomer, however, since Flash is actually downloading separate video and audio streams, buffering them and then reintegrating them.
While you might wish to avoid use of Adobe Flash due to security issues, such as were addressed in the two separate releases (v. 184.108.40.2067 and 220.127.116.116) this past week, these are your options:
Install Adobe Flash for plug-in based browsers from http://www.adobe.com/products/flashplayer/distribution3.html to view YouTube in Firefox. If you wish you can set Firefox to "Ask to activate" from the Add-0ns Manager Plugins tab.
Install IE Tab 2 Firefox extension, and watch YouTube from within an IE window in Firefox, https://addons.mozilla.org/en-US/firefox/addon/ie-tab-2-ff-36/. As you state, it's IE running an embedded version of Flash under the hood.
If viewing real-time in Flash is not acceptable, use a third-party tool to download the audio and video streams, reintegrate them and save them in convenient format such as MP4. Downloading a file also shows fewer glitches when YouTube is heavily loaded.