As for the quoted definition, I agree that if this is your first exposure to abstract algebra, you'll need a moment to unpack the sentence, follow some links, and especially, read on. But that's not just Wikipedia; the blog post also takes considerably more than one sentence to explain what it is trying to say. You can't explain everything in one sentence.
For whatever it's worth, as a data point relating to a recent discussion on whether a university CS education makes you a better programmer or not: We literally started learning about algebraic structures in the first math class on the first morning of the first year of university. If you're going to program in a setting where algebraic structures (or data types!) are relevant, this university knowledge will help.
Finally, this blog looks very nice visually, but the "broken typewriter" font effect makes the code examples much too hard to read. It would be great if the ribbon in that typewriter could be replaced.