The article starts seemingly assuming you have no idea what a vector is, but after showing a few graphs opines "As you can see, a vector by itself is just a set of numbers". I don't think someone who didn't already know what a vector was and how to recognize a vector on a graph would see that. Reading the next sentence about coordinate pairs and referring back to the graph might get you somewhere I guess. It doesn't seem to know who the target audience is supposed to be.
Trying to teach people things that you use every day and have throughly internalized can be an eye-opening experience. If you're trying to teach someone how to count in other bases and discover that they never learned about exponentiation, you're not going to get away with just saying "it's repeated multiplication and the top number is how many times you do it; oh also anything to the zero power is one (except zero itself...), and also negative numbers do this... and fractional exponents do that...". They're not going to suddenly "get" exponentiation the way you do from years of experience from three minutes of offhand remarks.
 http://hentenaar.com/dont-learn-c-the-wrong-way (parts 3, 4, and 5 in particular have similar complaints)
I take it back, I first encountered matrices in 8th grade and then several times in high school. Standard curriculum in the US at least (or at least where I lived).
The problem is that that's never built upon and it seems many math teachers don't have a firm grasp on why matrix math is useful, much less the ability to explain its utility to typical ninth graders.
I encountered vectors later in Physics (which was the most popular class to take as the one required science elective in my high school) and in one of the AP Calculus classes (which a large majority never take)
Matrices were revisted in Algebra II, with nothing new relative to Algebra I except that solving the matrix equations we were given required using Algebra II-level techniques on scalars. I guess a bit of spaced repetition might mean that more people remember it, but overall most students just forgot about matrices right after the test.
A good read if you didn't follow any CG classes, or if those classes are a long time ago.
In that link he mainly goes into matrices (if I recall) and to get into dot product and cross product explanations check out his section on vector calculus:
Can we find some similar tutorials that show other applications of linear algebra?
Just check the maths courses at gameinstitute.com.
IMHO, this is more a way to make people (game developers) feel mathematics intuitively.
It is somehow the same as the setosa.io approach which is all about visual explanations.
This is pretty cool.
You can make someone understand maths by demonstrating cases where you would actually need maths (here, gamedev) but it doesn't refrain them from going deeper and dive into details, which would achieve their understanding of mathematical concepts.
The first step is to get the global idea (and I give you the point for setosa) but even getting imaginative wouldn't permit you to fully use these concepts if you didn't apprehended deeper points on those.
As a grad student, I had a friend of mine who was teaching that same linear algebra course. I provided her with a lot of materials (similar to this) to help her students better understand different aspects of the material. There's a reason why the different introductory topics are taught, but often you don't really understand the topic until you get deeper into the applied material in 3rd and 4th year.