I was able to see the video in miniature; when I went to full screen, the screen went blank. Nevertheless, I see that I've followed your (standard) instructions to download Flash Player, but I lost you when you opened up Library. The only Library that I have in Applications holds fonts. Also, in my Applications folder I do have a Flash Player folder under Adobe; the problem is that the only thing in the Flash Player folder is a folder with "Addins."
You'll want to look for Flash Player in /Library/Internet Plug-ins/
You can ignore the folder in your Applications folder.
As long as you followed me through the installation steps, you should be good. When I opened the /Library/Internet Plug-ins folder I was just illustrating were the files were installed to.
Assuming you are on Safari, can you please verify that "enable plug-ins" is checked in the security tab of Safari's preferences dialog?