Helped is probably the wrong word. I mean't that the aircraft had a lot of excess speed to get back into the air again, had it been at a normal approach speed you would probably have slowed down enough that it wouldn't have been possible to get it flying again.

There's a decision point past which your option to abort is no longer viable. Think of an overloaded plane attempting to take off. It may need 400 meters to brake. If the pilot continues to attempt to take off until only 200 meters of runway are left, braking is no longer an option.

In the case of the landing attempt above, reverse thrust and the very sketchy (ahem) landing configuration would typically bleed off too much speed to make a successful takeoff possible. Depending on the runway the implicit decision point might have been behind them virtually upon touchdown. With so much excess airspeed, though, while a safe stop was not possible they were still able to fly. It would have been a hell of a ride, though, and just thinking about abusing an airplane like that kind of blows my mind.

But would also mean there was more energy to be converted to lift when the plane increased its attitude to take off again :)

More engine damage, probably.

But the excessive speed is what allowed the plane to lift off again.