Thank you for posting that link. From that web page:
The critical part here is "who wishes to enter the Kingdom"
However, the discussion in the context in which you made your post is not about a foreigner who wishes to enter Thailand; he is already in the country. He goes to his local immigration office after a visa-exempt entry or after entry with a visa other than a non-immigrant visa to apply for a non-immigrant visa with the form TM.86 APPLICATION FOR CHANGE OF VISA or the form TM.87 APPLICATION FOR VISA (where on both forms "visa" is a wrong translation of the Thai text ลงตรำ, which in the context of these forms means "arrival stamp"), as the case may be, to subsequently apply for a one-year extension of permission to stay for the apposite reason.
TM.86 Application for change of visa.pdf
TM.87 Application for visa.pdf