Most AWD systems do not have the ability to vector torque like that. They're usually based on mechanical limited-slip differentials that require some amount of slip before they partially lock, and sometimes the limited slip is only between front and rear, not left and right. There are different types, with some requiring a lot of slip before they lock up and others requiring little.

Limited slip differentials cost more than open differentials. Limited-slip differentials that lock up quickly cost more than those that allow a lot of wheelspin. Electronically-controlled torque-vectoring differentials cost yet more.

The system you describe seems to meet the NPS definition of 4WD someone linked elsewhere: "a means to mechanically power both front and rear wheels at the same time", though I wonder if there might be some more technical regulation with specific requirements. I agree that sort of thing could work well for off-road use.