I disagree with your disagreement. The article is based in the “non commutativity” of some operations. Multiplication of two real numbers are commutative, but, for example, if we deal with vectors, or with matrix, as she mention after, the multiplication can be non-commutative. This is NOT a property of the operation multiplication itself, but a property of the operation acting in a set, or more specifically, the property of the group. I guess she used wikipedia definition just to make it more clear, otherwise it would need a lot of concepts of abstract algebra.