That looks like a good link but it seems to be connected to the VLC player which is great too but isn't needed for viewing flash videos online. I'd recommend only downloading flashplayer from Adobe.
Always be wary of sites asking you to download a new version of flash player and/or "needed codecs" for viewing video files.
Chances are very good that it's malware.
And no, you don't have to delete the old versions of flashplayer.
Adobe Flash Player - Downloads