I understand that the author understands that "that demand" is tourists. What I meant is that you can't measure the amount of demand (tourists) by looking at the amount of supply (restaurants), which the author does.
That's not a sound way of thinking about economics.
Seeing that a certain level of supply remains stable over time tells you a great deal about the amount of demand present.
Of course it does. Much like looking at the skyline allows you to make some basic assumptions about aggregate demand for office space in Manhattan versus Kearney, Nebraska.
Except where it doesn't work, such as in the restaurant business, where some non-trivial percentage of the supply is superfluous and will go out of business. Of course, they will be replaced, so there is an argument that it is at least stable, even despite the high turnover - perhaps that's what you're meaning?