This isn't about desktop vs web apps. Plenty of desktop apps (or mobile apps) use a centrally located database server side.
So, #3 (synchronize between clients) is about merging data using CRDTs in a distributed manner without requiring a centrally located database.
A better way to think about it is Google Docs (as a desktop app or web app really doesn't matter), and it offers real-time collaboration on a single doc between users without using a centrally located database.
A better way to think about it is Google Docs (as a desktop app or web app really doesn't matter), and it offers real-time collaboration on a single doc between users without using a centrally located database.