I thought the quote was "what the Gods would destroy, they first make mad" meaning insane. I could be wrong - but I've never heard "they first make angry" meaning pissed.
I'm sure my Freeper friends will correct me.
Lycurgus "When divine power plans evil for a man, it first injures his mind."
Sophocles "Those whom God wishes to destroy, he first deprives of their senses."
Euripides "Whom God wishes to destroy he first makes mad."
Seneca "For those whom God to ruin has designd, He fits for fate, and first destroys their mind."
Your understanding of "mad" is spot-on.