Bless you, Joe Offer! No, this is a FANTASY. I ought to look up Williams' copious narration/commentary in the play, and just quote it. The Internet is not helpful here, and what I can pull up is in little bits and pieces.

"....a tropical seaport that bears a confusing, but somehow harmonious, resemblance to such widely scattered ports as Tangiers, Havana, Veracruz, Shanghai, Casablanca, New Orleans. "

A battered old map, in the possession of a character who stumbles up to the gate, has a direction on it, which is read out loud as part of the dialogue.

"Continue until you come to the square of a walled town, which is
the end of the Ca-MI-no Re-AL, and the beginning of the CA-mi-no RE-al.
Halt there, and turn back, Traveler, for the spring of humanity has gone dry in this place, and there are no birds in the country except for wild birds that are tamed and kept in cages."

The play on accents/ languages is essential here. The proper name Camino Real is given twice. The first time, with a good Spanish accent, meaning the royal highway.
But the second time it has an Anglo accent, a la John Wayne.
And to my ear, Williams is making a pun out of the second word. It is the Spanish word for "royal," but it has a different pronunciation and meaning in English.

What transpires on this dilapidated town plaza, with its dried up fountain, is all dream and part nightmare, as there are some actions which are violent and nihilist. So this is a landscape of the mind and psyche, with no bearing on a historical Camino Real, I'm afraid.