February 17, 2159 (one year later if you've sent the Utwig and Supox on their mission against the Kohr-Ah), the Kohr-Ah have won the doctrinal war.
7 days later, the Kohr-Ah will begin their death march, starting with the Druuge. The Kohr-Ah travel with a speed of 15.8 standard HyperSpace units per day. Once the Kohr-Ah fleet reaches the fleet of the victim race, the latter is destroyed instantaneously.
The Kohr-Ah then immediately begin moving towards the nearest race with a fleet, until all of them are destroyed. Then they will head for Earth. When they reach it, the game is over. The exact time depends on where all the fleets are at the time of the cleansing, and how many fleets are still remaining, but it's somewhere in the last quarter of 2159 (or 2160 if you earned an extra year).