The animated demo shows this perfectly. The bar which is showing the progress in the proof of work could just be a simple timer, and it would look exactly the same.
The back end generates the page, and makes a note of the current time. Then it doesn't accept the submission until N seconds have passed since that time. The animated bar on the front end is just for show; the browser isn't what is enforcing it.
Proof of elapsed time requires nothing from the other party. If I want proof that you spent at least 30 seconds waiting from the moment I gave you some starting signal, the only evidence I need to trust are the readings of my own stopwatch.