It’s not.
Mathematics is fundamentally about relations. Even numbers are just a type of relation (see Peano numbers).
It gives us a formal and well-studied way to find, describe, and reason about relation.
Eh, but you can also say that about philosophy, or art, or really, anything.
What sets mathematics apart is the application of certain analytical methods to these relations, and that these methods essentially allow us to rigorously measure relationships and express them in algebraic terms. "Numbers" (finite fields, complex planes, etc) are absolutely fundamental to the practice of mathematics.
For a work claiming to do mathematics without numbers, this paper uses numbers quite a bit.