Why do some rolling pins only have one handle?

As Megha says above, this kind of rolling pin is rolled by pressing on the pin itself, as you can see in the video. I have two such rolling pins in different sizes. The knob is not used when rolling out dough.

The single knob is there for picking up the pin, both by itself, and for transporting rolled pasta, pizza, and tart crust dough. In the video, you can see Sra Simili rolling up the dough around the pin, and using the pin to move it. If the dough has been stretched large enough to be the length of the pin, then you use the knob handle so that you can still pick it up.

The knob is also a useful handle when you use the pin to chase children out of the kitchen.

The description says that rolling pin is overlarge, I think that is the answer. A longer rolling pin would simply not be comfortable to brace with one hand at either end, and it would be more difficult to bring pressure to bear (in the case of stiff or stubborn doughs).

To use it, I would assume one's hands would rest on the pin itself and roll it under one's palms - similar to the handle-less rolling pins, those with flat edges (simple cylinder) or those with simple tapered edges. It lets the person exert their strength nearly directly on the dough, since their hands are closer to their center of balance. It's also an older, simpler style of rolling pin - historically much easier to find a stick or dowel to roll with, while making a rolling pin such that the handles rotate independently takes more skill (and thus is easier to break). So it may simply be a heritage style of rolling pin.

Why would this be useful? When rolling, the edges of the pin make a difference - they can cut into the dough if the edges are too long for the pin, since the pressure cutting off effectively leaves the edge of the cylinder an almost-sharp edge. A longer rolling pin like this would be able to work on larger sheets of dough, which would help in bulk applications or perhaps in some specific recipes where a very large dough sheet is needed for whatever reason and joined edges would be fragile. Exerting more direct pressure would also probably be useful when making larger sheets, the larger amount of dough would likely start off being harder to work with, thicker and more resilient from sheer volume.

A better question might be why have the knob-handle at all, though I'd guess it's still useful if carrying the rolling pin by one end, or grabbing it out of storage, or something. Or even just visually identifying it as a rolling pin so it isn't mistaken for scrap wood, a dowel, or something left-over from, say, construction rather than a legit kitchen tool.