As well as journals of physics, in peer-reviewed articles written by quite serious theoretical physicists.
“dimension” here simply means another degree of freedom that is “orthogonal” and independent of the previously known one(s).
You are using a definition couched strictly in narrow mathematical terms (much too narrow even for math, really). But the mathematical representation stands for quite real physical dimensions just as real as the lower three, if not visible to us (neither is the third dimension visible to the mythical flatlanders).
I always had a problem with flatlanders. I think that they wouldn’t be able to ‘see’ anything. any object in two dimensions would have no thickness, so anyone operating in those two dimensions could not make out anything about other two dimensional objects.