I checked to see if there were similar problems reported and only found some from a few years ago that were more related to iweb.app pages.
On your own machine it may have to do with file preferences. Most file extensions are set to use a specific program (or app) on your computer by default. If that program is not available in Safari, it would prevent playing. If you can find the file you're trying to play in Finder and view information it will list the apps that can open that type of file and you can (possibly) add Safari to the list of apps.