From your link, it actually says $2.99 per 1000 ReCaptchas so $0.30 for 100. Still cheaper than the automated method of the author.
Also, the automated method is probably more reliable than humans and much faster. And the cost of the speech-to-text API could be lowered by using cheaper services or an in-house model.
(Looking at other services, they all seem to agree on the $0.20-$0.40 range, mostly dictated by the hourly wage of their workers)