I'm curious how many people assume the same, as it seems to have become descriptively defined as any wordplay based on a dual-meaning.

Typically, I'm a fan of nuanced definitions because it makes language more useful but, in this case, I'll probably keep using it the same way because I don't feel that the sexual requirement adds much value.

'Pun' probably works in most cases but not all puns are double-meaning and puns also have a cornier/less clever connotation IME.