Photostory runs under Windows OS. Your chromebook runs Chrome OS so I think it extremely unlikely that PS will even install, let alone run, sorry!
OTOH, I suspect you could render and export a PS project from your Windows PC, transfer the resulting video file to a pen drive and then to your Chromebook (I believe it will have at least one USB port?). Assuming it also has software which can play video files (I think .mp4 format would be best) you can then use it as a file player for your project. For projection on a large screen TV your Chromebook must have a suitable connection socket (?HDMI) which you can use to connect to the TV.