I've looked at the excerpt of the screenshot of the page on the website of the Thai embassy in London you posted and see that it has the date stamp of 28 August 2019 with an update on 16 October regarding the temporary change of the vis-exempt permission to stay from 30 days to 45 days.
The text about the limitation of maximum three visa-exempt entries for 30 days (VE-30) by air and two by land is shown to apply to the VE-30, which is understandable because this outdated webpage does not take into account the new 60-day visa-exempt entry (VE-60) available now.
Therefore, I would say that it is incorrect to refer to this text as a currently valid rule, regulation or law applicable to the VE-60.
For information about the VE-60, we must refer to the Announcement of the Ministry of Interior, issued under the authority of the Immigration Act. This makes reference neither to unlimited entries nor to a limited number of entries.
It is tacitly understood, however, that all entries into Thailand are subject to Section 12 of the Immigration Act.
Sources:
Immigration Act, English translation:
https://aseannow.com/applications/core/interface/file/attachment.php?id=991237&key=afcda8a9154676f45da42331902f33c8
60-day visa-exemption, original Thai text
https://ratchakitcha.soc.go.th/documents/37563.pdf
60-day visa-exemption, English translation
https://drive.google.com/file/d/1LsZZ2J7z5jI1S2HEKAcljhbyn34L--VM/view?usp=drive_link