Those apps will still show adverts, publishers will still get paid, and advertisers will still pay to show ads. The only thing that needs to change is the way Facebook choose which adverts to show. Instead of an algorithm based on huge swathes of personal data that they've tracked it'll need to be a simpler "what categories of ads should we show in this app?" form. Adverts will be a bit less effective, which could drive revenues down a bit, but the sky is not falling on the ad model.
The real thing that Facebook are sad about is the fact that they will no longer be able to sell access to the tracking data. That's a lucrative business, and it's one that only really benefits Facebook and data brokers. Cutting off their supply of tracking data isn't a bad thing.