It's error-diffusion dithering. You maintain an error accumulator from one pixel to the next, which keeps track of your departure from the desired slope, and you make a diagonal rather than paraxial move when it overflows. (Or is that only DDA?) But I guess you're right that the position isn't being dithered. It's the slope.
I'm tempted to try the wobbly algorithm now to see what it looks like!
The cool thing about Bresenham is that you're constantly picking the pixel closest to the desired slope but you never have to do the explicit division of deltaY/deltaX. The division happens implicitly as you draw the line, using only addition and subtraction of integers. Which was quite handy for the primitive computers circa 1960 when Jack Bresenham invented it.
You mean the desired position. If you were always picking the pixel closest to the desired slope, your lines would all be at multiples of 45°.
I agree that the lack of division is surprising and beneficial.