See if I can take a reasonably coherent shot at it...
The pinion gears DO rotate on that shaft. As either side-gear turns, the pinion gears MUST move in opposite directions.
The shaft on which sit the pinion gears is fixed to the differential case and thus, of necessity, the shaft-and-pinions turn with the differential case and its drive gear.
When the tractor is driving flat and straight, neither the pinion gears, or the side gears (with the differential shafts), move in relation to each other, that is, the pinion gears do not, at that time, rotate on the shaft. Rather, they act as if they were all 4 welded together, and the pinion gears "drive" the side gears without any rotation on their shaft.
Of course, if the tractor were to only go straight, those gears COULD be welded together!
Even then, when a tractor turns and the back wheels go slightly different speeds, only then do the pinions rotate on their shaft, and only enough to allow the side gears (and differential shafts) to move at different rates from each other.
It"s counter-intuitive, because typically, one could expect "gears" to "spin", or be constantly rotating on their shafts.
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Today's Featured Article - The Cletrac General GG and the BF Avery A - A Bit of History - by Mike Ballash. This article is a summary of what I have gathered up from various sources on the Gletrac General GG and the B. F. Avery model A tractors. I am quite sure that most of it is accurate. The General GG was made by the Cleveland Tractor Company (Cletrac) of Cleveland, Ohio. Originally the company was called the Cleveland Motor Plow Company which began in 1912, then the Cleveland Tractor Company (1917) and finally Cletrac.
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