The multi-engine, mechanical transmission, complex gearbox approach is of course just a variation on what turned out well with the mass of diesel multiple units of the same era, where a three-car branch line train had four engines, two under each power car, and four somewhat complex gearboxes to go with them, all derived from mass-produced automotive power trains of buses of the era.
Ah, but it's not the same! I don't think either the film or Wikipedia really explains what the Fell gearbox is doing very well.
You could make a locomotive on the same principles as a DMU, either mechanical or hydraulic. Say it too has four engines, with a hydraulic drive or coupling considered as part of each. Combine them using a gearbox that simply connects each input shaft directly to a common output shaft, and they all turn together. In a DMU the wheels and rails couple its engines in the same way. Total torque (or the equivalent traction force at the rail) is the sum of all the engines', if the gearing is 1:1 throughout.
A single differential gear (with 2 inputs) or the Fell gearbox (with 4) is different in important ways. It does not force all its input shafts to rotate together, instead the output shaft speed is the arithmetic mean of the 2 or 4 inputs. If the engines play nicely together and do run at the same speed, the output speed is also the same - but only if. It's not hard to see this for a single differential, just by imagining it (if you can do that sort of thing).
For torque, the situation is harder to see. Now, all input shafts must have the same torque, apart from small differences due to friction and losses. The output torque is 2 or 4 times this equal input torque. Think about a car's final drive to the wheels - you know if one wheel loses grip, the torque on the other wheel and the engine both drop to near zero, and that's the same principle applying. Locking a shaft, instead of driving it, leaves the torque the same but now no power is supplied.
The speeds of the engines at their common torque (depending somewhat on exactly what the hydraulic coupling does) will be determined by their torque/speed curves, and how they react dynamically to changes in load. I imagine the designers had no way of predicting that accurately, as you now might by modelling, so the trials were needed to find that out. The unusual turbocharging system was also, I suspect, meant to persuade the engines to play nicely together. If they don't things could get very messy!
