Evidently this image dates to the 15th century, and is found in the manuscript "Morgan 1045," from the backside of leaf 22, in the Morgan Library & Museum.

It seems that this book was partly intended for amusement and educational value, but this specific image may also be based on misunderstandings about what elephants were actually like, given their general non-existence in Europe. Then there's the castle, which may be an attempt to represent a "howdah" (i.e. elephant saddle), or may even have a chess-like implication. For example, precursors to chess arose in India, such as chaturanga / chaturaji, and elephants were major pieces in that game.

More quirkiness of this kind can be found here:
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