>What does "move their money" technically mean in this situation?

Sell GOOG and buy META (or whatever)

>Is this a threat of tanking the stock price by selling all $6B at once? TCI would hurt themselves too if they do that.

The act of liquidating their position is what reduces the price. So they drop their ask to the lowest bid price that liquidates their position net positive and in theory that action would cause a price cascade. It's a threat, not a guarantee.