Is this an example of a compound sentence?

I was reading an editor's blog in which they are discussing the different ways to start a sentence, and they classify the following as a compound sentence when analysing an example:

"Whatever anesthetic they used, it didn't take."

The author labels this as two independent clauses, and I'm very confused by that. I thought a compound sentence was like my preceding one, where two independent clauses, which could stand as sentences on their own, are joined by a comma and a coordinating conjunction. The example has a comma, but no coordinating conjunction. And I don't think "Whatever anesthetic they used" is an independent clause, because "whatever" is usually used to introduce a dependent clause, but I may be wrong.

Is there something I'm missing here?

Also, they say that there are no participle phrases in the passage even though it ends with this, which I'm pretty sure is an example of a present participle phrase at the end of the sentence:

"He kept it up as they twisted in the second, screaming all the way into blackness."

It was an otherwise useful blog, but these two things struck me as incorrect, and I wanted to check that it wasn't just a misunderstanding of the terms on my part.