The Super Mario 64 revival serves as a demonstration for Ross's Super Character Controller project for Unity. Ross worked to make it a fairly faithful re-creation, but he left out "some really minor stuff that nobody cared about like red coins or the Wing Cap or the Big Bob-omb," and replaced them with "crowd pleasers like giant springs and coin blocks."
The game works with several game controllers, Ross says, such as those for the Xbox One and Xbox 360, as well as Sony's DualShock 3 and 4 controllers.
As of this writing, the Web version appears to be offline. Ross offers a downloadable version of the game, though, and offers builds for Windows, OS X, and Linux. If you're a Unity developer, you can also download the project files and get a look at the source code.
Have fun, and enjoy this little flashback to an earlier era in gaming.