This is a pretty common joke/expression among mathematicians i.e. "As you all know from kindergarten abelian groups are just monoidal groupoids with a single object" or whatever.
I understand "vector calculus" here as meaning "how to compute stuff with vectors", i.e. adding and subtracting vectors, computing the inner product etc.; not doing calculus with vectors. Obviously both interpretations are possible, but the latter is usually called multidimensional analysis.
Surely (multidimensional) analysis is the term used in mathematics for a more rigorous investigation of the basis of calculus. In physics, vector calculus is taught as a tool and the course is called vector calculus (or maybe multivariable calculus.)
The book uses "calculus" several times to mean "derivatives and integrals"
Europeans
Even African
People who grow up to attend graduate schoool in the study of mathematical methods of physics
AP courses have vector calculus.
It was the last unit in senior math at my high school.
Probably anyone who took a more than introductory physics class. Not me, though.