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On an initial observation this appears to be the case.
However, the carts about which Darwin wrote during his visit to the Azores had a separate turning mechanism underneath the tray and not a fixed axle, which allowed for easier cornering.

As well, a pair of bullocks would tread the same path as the cart and being heavier, the cart would obliterate these hoofprints with its wheels.

Even if not a fixed axle, the large diameter, small width wheels of the carts could not make deep ruts in mud like the ruts we are seeing in stone. The upper part of the ruts should widen during sharper turns, because of the large diameter wheels, but they don't. For this same reason, the ruts in stone would break cart wheels when they hit a turn that wasn't extremely gradual.
This happens when the rut is deep enough that, if you measured along the edge of the rut from the front of the wheel to the back, you get more than 4 or 5 inches. If you have 12 inches of rut with wheel down in it, if that rut turns sharply it will break the wheel.

Everything I've read indicated these carts were single-animal pulls, but even if there were a pair of animals pulling and the cart wheels went directly through the animal tracks, the wheels aren't wide enough to obliterate the animal tracks. Cart/wagon wheels are a few inches wide at most. A typical four-legged beast of burden has hooves wider than that, and a stance much wider.

The ruts are artificial, but it seems highly unlikely they were powered by animals or people. Maybe sails? lol. I dunno.