Their patent (https://patents.google.com/patent/US4785361A/en) doesn’t mention a laser, but of course that doesn’t imply it wasn’t a laser.

I would guess (more or less) identically damaging multiple floppy disks in the same way would be easier with a laser than with something mechanical (e.g. a knife or a drill) (it is fairly easy to control power and duration of a burn), so it might well have been a laser.

On the other hand, disk tracks weren’t exactly tiny at that time in history.

Good question. I don't know the answer, but I'm quite certain that it didn't really matter what mechanism was used to mark a diskette. Any damage would be equally strong as a way to detect copying.