I believe he knows what compost is, he is just being lazy about using it interchangeably with what you find at most garden shops. Most commercial bags of garden soil and compost both contain a lot of broken down wood. He is just suggesting you shouldn't really have any organic matter around your roots, except for at the top level. It's good to promote mycorrhizal fungi but only at the top layer etc
I think he mostly ranting about how commercial gardening places just sell "soil" that is mostly always comes with added "compost" e.g. https://shorturl.at/mvwzG
Where as they should sell more clay/silt/sand mixes and encourage top dressing instead.
Most people just fill their pots to the top with those bags and it leads to adverse effects.