As others have pointed out, Linear Algebra is very relevant in economics. I would say that it universally the most useful "higher-level" mathematics (i.e. excluding basic algebra), both in terms of applications and in studying other higher-level math.

But, as you point out, it is not obvious why the focus is on vector geometry. To understand this, you need to know a bit about Linear Algebra. At least at the elementary level, it is a very much a mix of algebra and geometry. However, it can be taught, and often is taught, only from the perspective of algebra. In my experience, this just results in most students being confused by the material, both in terms of understanding the content and its actual purpose/motivation. By teaching the geometry, and getting students to think in terms of the geometry, they actually understand the algebra better.

Now, in this particular case, it is not clear if this is exactly the intent of the class. It seems even somewhat more focused on geometry than I personally think makes sense, so the intent might be different (no way to know without context, of course). Nevertheless, you'll likely find it gives a solid foundation in a very important field of math.

Lastly, I'd like to elaborate on why it is helpful to focus on geometry in studying algebra. As MPW pointed out nicely in the comments, framing things in terms of geometry helps with intuition. That is, while you can and should develop intuition for algebra independently, geometry provides a convenient and deep source of intuition, taken from everyday life. This really helps in understanding the (generally quite abstract) concepts of Linear Algebra. It's always good to use previous knowledge to understand new material, and this is no exception. It's even valuable later when you have the algebraic intuition to see how the two match up and compliment each other.