The ActiveX plugin in Windows 8 is now a proprietary Microsoft build and it can ONLY be updated through Windows Update, be it on a desktop or tablet. There are two different Flash Player plugins for Windows, but the ActiveX cannot be installed via download from here. The other can. It's here: Flash Player Plug-in (All other browsers)
See also: http://helpx.adobe.com/flash-player/kb/flash-player-issues-windows-8.html for more steps.