I can't really find a good definition of the engineering sense in a dictionary but if we start from this sense of scale:
a ratio of size in a map, model, drawing, or plan.
"a one-fifth scale model of a seven-storey building"
So I can buy a 1:100 scale model ship or a 1:50 000 scale map. If I buy a scale model I expect it to accurate, apart from the size.
In engineering and science, as your original text says, it means "proportional to" or "approximately (linearly) proportional to". For example, if I say: "The heat loss in a fusion reactor scales as the surface area of the plasma but the heat production scales as the volume" that tells you that large fusion reactors are better.