Headless does not mean “no screen anywhere.” It means you are not required to use the company’s app or site to finish the job.
You might say: “Book a flight and a hotel in Tokyo.” A helper (with hooks into services, e.g. MCP or other agent APIs) talks to airlines and hotels for you. You might never see their homepage or their “join our club” popup.
Whilst I can see where the author is going with this, I can't see some tasks, particularly booking concert tickets, being done by AI agents. Whilst it may be convenient for end users, it's also open to exploitation by scalpers.