Ok, this makes sense. I must have been using a client that had 'Zap' icons and because I didn't have a Zap balance I just assumed the buttons didn't work because I had no balance.

I didn't realize every single person who downloads a zap-supporting client had to also set up a separate app to handle the micro-transactions and host that app somewhere where it is available 24/7 in case their post gets zapped.