The prototype for SUPERHOT was created for the 2013 7DFPS Challenge by the SUPERHOT Team. It was extremely popular, and won the WGK2013 Developers Showcase. Its success encouraged the development of a full version of SUPERHOT. The game features a single weapon, the Pistol, and only Standard Enemies. There are only five levels. It is built in the Unity Engine.
Each level starts with the title of the level flashing on the screen, and ends with the words "SUPER HOT" flashing accompanied by a robotic voice reading the text.
It can be played for free on the official site.
At the time it likely had nothing to do with the story we got from the full release but it can be linked through versions of THE SYSTEM.