His words: This suggests that learning and doing mathematics might play an important role in educating future computer professionals.

Your words: some amount of math is helpful.

Do you not see how these are the same idea, abstractly?

Also, "if we define mathematics as 'handling abstractions in a precise manner'"

That IS the definition of mathematics. The author is not arguing for more calculus. His background is mathematical logic which is a standard course before all "real" math (analysis, topology, abstract algebra). All of these subjects handle abstractions in a rigorously precise manner.