I am afraid that you are right, you are no engineer!
Regardless of the towing load, the maximum torque being fed through the box is dictated by the engine. It is input torque (from the engine) that will damage the'box. The maximum towing capacity is as more about tyres, suspension and brakes than engine power. My RS6 has only a marginally higher towing capacity than a 2.0 litre A6 - and that is despite bigger brakes, air suspension and 4WD.
Sure, towing stresses a 'box - it is likely to get much hotter (properly prepared towing cars have additional oil coolers for the gearbox - MB fit them when you spec a tow bar, but I don't know if Audi does), and the engine will be feeding more torque and power through the box than it would on an equivalent journey without the trailer, but the gearbox is fundamentally up to the task of towing.
Expanding out on the OP's topic of a tuning box, some gearboxes (including the ZF 8-speed - maybe other Audi boxes, too, I don't know) can measure and store data on when they are being over-torqued (by a tune, for example). This data can -
and has been - used in warranty claims to reject a vehicle repair, so, if an owner fits a tuning box, they should be prepared for the possibility of a TD1 flag and / or a rejected warranty claim. I understand that the main ECU also shows trace data of where a tuning box has been fitted even after it has been removed for a dealer visit, but I have no direct experience of this through my work.
My personal feeling is you would have to be insane to fit a tuning box to a car that is under warranty now that ECUs are so sophisticated and knowing that vehicles with engine and gearbox failures are now examined minutely for signs of chipping by Audi, but I am aware cases of rejected warranty claims and TD1s being issued so I am naturally cautious.