Think of it like this: how would you test the vehicle without a crane? They are testing out the powered landing capabilities so the idea is to work with slow, smooth trajectories that may be mostly vertical but will obviously incorporate some lateral movement too.
If anything were to go wrong the vehicle could diverge wildly off-course and probably necessitate self-destruction. Instead, the crane allows you to hold onto the vehicle with (ideally) minimal reaction between the cable and the vehicle.
Of course without any thrust the cable provides a reaction if the vehicle is hanging, but once the test is being run they will likely be adjusting the tension to be minimal (while being careful not to let it go completely slack).
The overall idea is like putting a leash on your dog so it doesn't run away, but still giving the dog slack to walk around comfortably (at least if your dog doesn't try pulling you around like mine!).
As for the overall thrust and throttling, this system is being designed to operate with thrust that reduces to less than 1 g acceleration (otherwise landing would be too dangerous since you would depend on shorter high thrust burns while still descending). That article you link to actually states the dry weight is 14000 lbs, so considering 4000 lbs of propellant you end up with a mass of about 8100 kg so an acceleration of about 1 g.
This document gives some more details about the DragonFly vehicle although it is primarily concerned with the subsequent 4 test phases after using the crane.
From this document we can pull out these numbers:
Dry mass = 6364 kg
Propellant mass = 1756 kg (assuming full 400 gal tank with 50/50 NTO and MMH which have SGs of 1.44 and 0.88 respectively, although it could be anywhere from 1332-2180 kg)
Maximum thrust = 546.7 kN
On page 97 they state "The four engines are modeled as a...", which could be just some confusion about the fact that the engines are configured in pairs, but might also suggest they are only firing four of the engines.
With the masses I've quoted, you would need a thrust of about 79.7 kN to hover, which corresponds to a throttle of 14.6% for all 8 engines or 29.1% for 4 engines.