Typically, the API is a screen recorder and the CAPTCHA is sent to thousands of workers who essentially mini-remote-desktop in and solve them for about 80 cents/1k CAPTCHAs. Here are some other, similar services: https://0captcha.com/, http://bypasscaptcha.com/, https://deathbycaptcha.com/
I'm surprised these players are still around. They've been operating for nearly 20 years back when I had discovered them.
The entire industry is actually not completely as black hat as you might think. Yes, it's used for spam and botting, but at least at the time a lot of people used it for bulk downloading, which is how I discovered it. Additionally, it does provide work for the poorer parts of the world.