I’ve got Hyperspace to work on Chrome’s Native Client. The advantages of that are that it runs very fast (much faster than the Flash version or a WebPlayer version) and it will also work in Linux!
Here are the steps to get this to work:

1. Get Google Chrome
2. Enable NaCl by going to chrome://flags, scrolling down (or CTRL+F) to Native Client and pressing ‘enable’.
3. Restart Chrome
4. Play Hyperspace here.