Rome fell in 476. The seat of empire moved to Constantinople. When Constantinople fell to the Ottomans in 1453, Moscow claimed to be third great empire. Around 1510, Philotheus of Pskov warned Grand Prince Vasily III: if the Third Rome fails, there won't be a "fourth" instead there will be an antichrist.

Thiel is referencing this but saying that the US is Rome and if it falls (i.e. too many socialist policies are enacted and there is too much democracy such that Thiel and other billionaires don't have enough power) there will be an antichrist.

In Thiel's view the antichrist will also be a democratic socialist and the only way to avoid this awful outcome is to give billionaires more money and power.