I spoke too soon. The system with both v15 like you showed will now play video in the browser but it will not cast to the chromecast. Content other than the video will cast though. Our other system showing v 15 and v11 below works without any modifiction.
Adobe Flash Player(2 files)- Version: 15.0.0.152
Shockwave Flash 15.0 r0
Name: Shockwave Flash
Description: Shockwave Flash 15.0 r0
Version: 15.0.0.152
Location: C:\Program Files (x86)\Google\Chrome\Application\38.0.2125.58\PepperFlash\pepflashplayer.dll
Type: PPAPI (out-of-process)
Name: Shockwave Flash
Description: Shockwave Flash 11.9 r900
Version: 11,9,900,170
Location: C:\Windows\SysWOW64\Macromed\Flash\NPSWF32_11_9_900_170.dll
Type: NPAPI
MIME types: MIME type Description File extensions application/x-shockwave-flashAdobe Flash movie.swfapplication/futuresplashFutureSplash movie.spl