It's not quite so clear-cut. We even have a historical precedent here:

https://en.wikipedia.org/wiki/Craigslist_Inc._v._3Taps_Inc.

In that case, the court found 3Taps was criminally guilty for scraping publicly available craigslist data while logged out because 3Taps knew their use was not authorized.

This person has just received an email from Yelp telling them their free usage is not authorized, so circumventing that may well be illegal, now that they've been given that sort of communication, even if it might be questionably legal for other serpapi users.