Keep in mind the method outlined in the AIMMS book is a only an approximation for case of two continuous variables.
Bilinear constraints frequently come up in chemical process applications. For example, decision variables for a particular process stream might be stream flow rate and concentration of a species, and the constraint written on flowrate of that species. These situations lead to non-convex solution spaces that can be solved using global optimization techniques.
One way to treat these situations in a linear programming context is to replace the constraint with a set of four linear constraints that provide a convex 'outer approximation'. The outer approximation itself has been known for a long time, and is sometimes called 'McCormick Relaxations.'