Thank you for posting this additional information. No need for posting scans or photos of the stamps because the founder of this forum, formerly knows as ThaiVisa forum, surely knows what he has been shown by this Brit.
Another member already quoted some text, source not given, indicating that the requirements listed by the Department of Employment includes a non-O, without limitation of the reason for which the non-O visa or the one-year extension of stay was issued. I clearly remember having seen this list and with that requirement some years ago but try as I might, I cannot find it now on their website.
My conclusion is that whereas it may be true that some or all branches of the Department of Labour have in some or all cases refused to to issue a work permit to the holder of an applicant with a permission to stay for the reason of retirement, if such application has ever been made in such circumstance, there is no legal obstacle for the Department of Labour to do so.