Presumably you already constructed points A and B and joined them into a segment, so there's now a point B to miss.
Of course, it could be the case that there’s a multi-step proof where you do care about the positions of A and B in relation to some other things. But I think that would require doing the analysis with that in mind. Maybe the order in which you construct the more complicated proof can also benefit from picking certain points to be exact.
I think it is possible that part of what’s missing in your “given a line to..” is that the description of the line in the .. refers to A and B, or possibility the phrasing is just informal.
Then to start the construction, you have to put one arm of your compass on the point A, and one on the point B. These points exist and are already marked, but you incur error when you place your compass down on each one. These are the represented by the blue and yellow circles in the diagram.
That line segment isn’t defined, it’s postulated (“there somehow is a line segment with endpoints A and B; you needn’t care how it came about”)
Also, is the inaccuracy around B actually a circle? I think you could easily end up missing that horizontal line he’s added between the imagined “right A” and “right B.” But, that line shouldn’t exist yet, it connects A and B wherever they are. The position of B is wherever your pencil lands.
The second circle seems to have more room for error. You can miss B with the pointy end, and could flex the compass differently from when you did the first circle, resulting in a different BA distance. Although, it should be possible to visually check this.
Is that right? I somehow never managed to take a geometry class.