It's an intriguing idea, but the scope of any such formal definition would essentially be the entire scope of physics, materials science, thermodynamics, etc. For much more bounded problems (like that very fun website you linked) I think something like that would be more attaintable, but still challenging.

Take the example of the differential gearing shown. I doubt there exists any functional differential/mass produced assembly that looks exactly like the example presented. The concept of differential gearing may be able to be broken down into more symbolic representation of forces and motion, but at some point it becomes simplified to the point of impracticality.