These services would accept your Bitcoin deposit, add it to their pool of funds, and then send you different coins from their pool, minus a service fee. For a time, this way an effective way of obfuscating the origins of your funds.
With how sophisticated blockchain analysis has become, such basic techniques don’t work. Chain analysis might not be an exact science, but it can be highly accurate when dealing with such rudimentary and unsophisticated methods of mixing.
Your article suggests swapping to Monero and back to BTC, but this is also very basic and chain analysis has several data points that can be used to unmix your transactions.
Coinjoins are still very effective but your level of privacy will depend on the amount of collaborators you are participating with and on user’s post-mix behavior.