No, you do not get a Steam key when you buy it on Itch. Last night I bought MidBoss and Caves of Qud. Midboss has a very clear place to get a Steam key (the bottom of the downloads list). Caves of Qud does not give out Steam keys. I bought it with the assumption that a random stranger on the internet would not lie about this, so thanks for misleading me and adding +1 to my misanthropic tendency, I guess.
I'm totally happy to be proven wrong, though.