Delta-v to launch from the surface and dock with the space elevator, according to the article: 0.52 km/sec.

Delta-v to launch from the surface into Martian low orbit: 3.8 km/sec.

So less than a seventh as much velocity change. Now let's use the rocket equation. A methane rocket has specific impulse of about 370 seconds (that's a measure of how fuel-efficient the rocket is). We'll use a starting mass including fuel of 10,000 kg.

For a delta-v of 520 m/sec, we get a final mass of 8380 kg. We only had to burn 1620 kg of fuel to get 8380 kg of rocket and payload up to the elevator.

For a delta-v of 3800 m/sec, our final mass is only 2748 kg. We had to burn 7250 kg fuel, to put only 2748 kg of rocket and payload into orbit.

Assume in both cases that the rocket is 1000 kg, then with the space elevator we're getting 7380/1620 = 4.55 kg payload per kg fuel, and without the space elevator we're getting 1748/7250= 0.24 kg payload per kg fuel.