The line you quote from Wikipedia is not the definition of a nonlinear system.
EDIT: The definition depends on the area of math you are working in. The definition of a nonlinear system of differential equations is different than the definition of a nonlinear system of polynomial equations in commutative algebra. As far as the article in question it's an accurate description of the problem and why it's a big deal.
EDIT: The definition depends on the area of math you are working in. The definition of a nonlinear system of differential equations is different than the definition of a nonlinear system of polynomial equations in commutative algebra. As far as the article in question it's an accurate description of the problem and why it's a big deal.