It’s very intentionally written from the perspective of someone who knows linear algebra but maybe not that much, if any, abstract algebra, because that’s what the target audience is. Not university math students or graduates, but highschool graduates, CS/physics/engineering students and graduates, game/graphics programmers and so on.
Yeah. It's written to teach people who do not have (what some might consider) the standard prerequisite knowledge. I have no doubt the author understands algebra over a field. The author recommends teaching Geometric Algebra as a pedagogy at the end
