Well, the booking service works exactly how they explain it should:
"‘Empty legs’ are flights that are due to operate without any passengers as the aircraft repositions back to its base, or is going elsewhere to be ready for its next assignment. If you can move quickly, an empty leg can be really handy.
If you were planning to head that way, you could hop aboard the empty leg and save up to 70% on the cost of a conventional private jet charter."
However, if you look at the prices, it's not exactly RyanAir or EasyJet, so puts empty leg chartering some way out of the reaches of the masses, therefore not exactly fodder for Expedia or the like. It's not just seats you're paying for, it's exclusive use of the whole aircraft.
Most company's like Air Partner get the heads up about empty legs via the operators themselves, or they try to "back sell" charters that they've already arranged. They can be a good deal if you're in the right place at the right time with a big enough wallet.