This is basic math, not advanced math. If you don't know it, don't worry, you can learn it pretty quickly. Maybe watch some 3Blue1Brown videos and do some textbook exercises and/or game programming. Git gud. There is no royal road to radio modulation.
I learned that subtraction was the same as adding a negative number sometime around second grade, and I learned (then forgot) the trigonometric angle-sum identities in tenth grade. And that was even with the handicap of having to attend school in the US.
And, just above the text you're complaining about, he even provides a straightforward geometric proof of the angle-sum identity! So you don't even have to know it to read the article! You just have to know what a cosine is! I learned what a cosine was in eighth grade because I wanted to program a game where objects would fly across the screen at a constant velocity but a varying angle. You can learn it too!
He's not, like, invoking the convolution theorem or anything in those quotes. Although he does get into it a bit.
I think that, if you know the convolution theorem and Euler's formula, things like the production of sum and difference frequencies from the multiplication of sinusoids start to seem obvious rather than sort of random. When I was in high school they seemed sort of random. My uncle had tried to explain Euler's formula to me, along with the Taylor expansions for sine, cosine, and the exponential, but I hadn't really understood, because I didn't have the background knowledge to appreciate them then.