He writes: A rich API provides methods for inspecting and controlling all available objects and their run-time and persistent properties. This makes it possible to replace configuration files with GUI tools. Many desktop environments provide such tools.

That is wrong, if I don't misunderstand it. It does not matter much for the possibility of GUI tools whether they talk to an API or whether they parse and write configuration files. That is stuff you abstract away.

It is of course possible that pulseaudio allows settings to be set that didn't exist before. It's API might be better for that - but that doesn't say you couldn't do the same with writing to configuration files if they had the same capabilities, like targeting a specific application (one of the use cases he mentions below).