First line of the Wikipedia page is fine: "In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input."
Scientific American's typical reader surely understands a) the concept of a function b) the concept of proportionality.
It's fine to say that nonlinear systems are difficult to analyze, or have a reputation for being difficult to analyze. But it's bad practice for a science communicator even to run the risk of giving people the impression that the difficulty is part of the meaning (definition) of the word.
Did the article change? The rest of the “hard to analyze” sentence you quoted above is “linear systems respond proportionally to changes in variables, whereas nonlinear systems have more complicated relationships.“
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.
Scientific American's typical reader surely understands a) the concept of a function b) the concept of proportionality.
It's fine to say that nonlinear systems are difficult to analyze, or have a reputation for being difficult to analyze. But it's bad practice for a science communicator even to run the risk of giving people the impression that the difficulty is part of the meaning (definition) of the word.