I checked my version and it was a wee bit away from the one that was to be downloaded. I therefore used your un-install link and got rid, then all hell broke loose. I could not install the new version because every time Adobe came up it was saying it was malicious and IE had prevented the page from opening. I have Adobe listed as an acceptable site, but that had no effect whatever.
Eventually, on a site that needed the Flash element, I managed to get it to accept the installation, when a window came up asking me to install it, by very quickly clicking on the download window and managing to get it to accept Adobe. This took an eternity to complete because of the speed the window closed and told me to go forth and multiply!
I think it has installed, but what a palaver. I shall wait next time and get it to do it automatically!
I have been to another site after searching for Flash Player 10.1.85.3 and downloaded that one which is listed as Flash Player Plugin 10.1.85.3. I also have a Flash Player 10 ActiveX which is listed as 10.1.82.76. I'll leave them both on, but presumably, the link you gave is the Plug-in one?