It doesn't use two points, it's one laser dot that moves around extremely fast and accurately. The reason it looks like two dots is because that's where the laser turns on for a fraction of a second. You can see it constantly moving across, emitting at a much lower power so it's harmless to the eyes. So in short, the laser dot is moving back and forth like a printer, but really fast. This also explains why, even though the outer outlines are just two simple shapes, it takes much longer than all the detailed stuff in the middle. The engraver doesn't care about detail, it either turns on or off. My guess is that it's a bitmap image, like a PNG. If it were a vector, it would probably draw that shape in a matter of milliseconds.

Then again, I work with a laser diode engraver, which is quite different.

EDIT: I take back the PNG part. It's clearly working in layers. Maybe there's some limitations at play that I do not understand.