Important: see “Final Update” below
Ender's Game was an experiment of ManaLocke's to test timing mechanisms, and is based on a (manual) design by SethBling. The device serves two purposes:
It is found, naturally, in the End. This can be reached by one of the two Zone of the Enders sites, which are in the DTA Nether tunnels.
Once in the end, take the bridge across to the main landmass, ascend (there's a staircase on the left), and head along the same direction as the bridge. The Ender's Game will be slightly to the right.
The instructions on its use are also included in a written book in a chest on-site. However, they are included here as well.
When finished, the cobblestone arrow points in the direction of the End Portal.
As of the latest revision of the laws of nature, endermen have evolved to possess a new sensory organ. This Darwinian boon allows them to detect when their skulls are attempting to coexist with dense matter, and triggers their autonomous teleporting instinct. As a result, the Ender's Game xp and pearl harvesting facility has been decommissioned.