I was a bit put off by the introductory chapter where he is using a lot of nonstandard terms such as "abstract species/genus" rather than the usual type theoretic treatment. However, take that as the remark of an ignoramus.
There are many different backgrounds from which to explore these topics, and type theory is just one way. Also the introduction isn't really trying to formalize computation itself, but give mathematical tools for talking about algorithms.
The abstract species/genus is probably inspired more by Aristotle than CS topics.
I don't think the terms "Abstract species/genus" ever came up, but it makes me think of Introductory course to Object-Oriented Programming (Java), lecture 5: Inheritance
There are many different backgrounds from which to explore these topics, and type theory is just one way. Also the introduction isn't really trying to formalize computation itself, but give mathematical tools for talking about algorithms.
The abstract species/genus is probably inspired more by Aristotle than CS topics.