"Riding on" can mean "depending on." It is often used when something big and important depends on something small.
"The election looks very close. Everything is going to ride on the vote in Grant County."
"Every dollar the gambler had was riding on the next spin of the roulette wheel."
"It's the first quad-camera high-end smartphone from Samsung and a lot is riding on the success of the device."
"A lot is riding on these studies, therefore it is imperative that at least one of them ends up being successful."
Buffett says that billions of dollars depend on the decisions made by short-term speculators. Figuratively, they are sitting at their keyboards, and when they decide to place an order, when they press the final key something will happen that could make or lose billions of dollars.