From this definition below, but also from common sense, ratio and interval data should fall under Quantitative. I find it surprising that the text you refer to classifies in this way - it would be useful to know the actual definitions that they are using.
There are different ways of looking at variable types, and it can often lead to confusion. Quantitative and Qualitative are both sometimes used as a "top level" classification, and that often leads to something like this:
Quantitative data deals with numbers and things you can measure objectively: dimensions such as height, width, and length. Temperature and humidity. Prices. Area and volume.
Qualitative data deals with characteristics and descriptors that can't be easily measured, but can be observed subjectively—such as smells, tastes, textures, attractiveness, and color.
Broadly speaking, when you measure something and give it a number value, you create quantitative data. When you classify or judge something, you create qualitative data. So far, so good. But this is just the highest level of data: there are also different types of quantitative and qualitative data.
From this definition, and also from common sense, ratio and interval data should fall under Quantitative.
I find the Quantitative/Qualitative distinction causes more confusion among students. For example, ordinal data has some characteristics that are qualitative and quantitative - they are often indexed by an integer, and although each value may not be a quantity, consider a variable "Size" that can take on values Small, Medium and Large. These are qualitative in nature, but they have a quantitative aspect because Small is smaller than Medium and Medium is smaller than Large. They are often indexed by integers (say 1,2,3) that provide further meaning but NOTHING to do with the distance between them (so nothing about how much smaller). In this example the distance between each is 1, but this 1 has no meaning, except for being positive, and it is certainly not possible to say that Large is twice the size of Medium, or anything like that.