If the speed of the horses depend on the machine's speed on which the game is running, you should check your timing instead of making a movie out of the game.
I don't see any solution rather than relying on the clients hardware and make the timing and the display initialization as robust as possible. Plus i suggest to offer different versions to download, i.e. one via webstart for people with Java installed and the Mac-OSX- and Linux-folks and one with a bundled VM for Windows for those, who don't care about the bigger download but about installing the runtime.
Distributing a game as a movie is, apart from the fact that i consider this to be hardly doable in a pleasing way,...quite...well...absurd (no offense... :wink: ). And even if it would work reasonable well, you'll run into other problems (caching problems, download problems, client problems with the video codec/card, bandwidth problems etc....).