A bit ironic, but I can't see any videos from the tutorials since it seems they use a plugin.
Well, they are youtube videos, so unless you haven't set your youtube account to use the HTML5 player, indeed it will try to use the Flash player.
That is up to the configuration of your Youtube/Google account as far as I can tell.
I have them setup as HTML5, in fact I don't have Flash installed on my browser (Vivaldi), or I wouldn't be able to see any Youtube videos.
Maybe this software is trying to force the plugin? This is how I see any video: http://i.imgur.com/ajIq9Yl.png
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Same here (except I have flash, it is just click to enable it), the player in the tutorial section uses flash instead of the "html5" player, perhaps it depends on how they are included or something like that? I'll leave a Tom tag just in case.