I think their point was that engineering is the process of finding the most efficient way to accomplish a given goal given the whole of science and technology with which to accomplish it. In this way, a purely mechanical watch attempting such complex calculations is suboptimal. As such, it's existence is a form of art -- it is engineering only in the sense that the restrictions imposed are themselves non-optimal (for instance, the requirement that purely mechanical mechanisms be used). Something at the pinnacle of engineering would seek to optimise not only the solution, but also the requirements.
Why is engineering restricted to finding the most efficient way? That sounds straight out of the critiques of the Cult of Efficiency. In my opinion, Engineering is a process applicable to any goals, efficiency being just one possibility; hence I much prefer Wikipedia's definition:
Engineering is the application of mathematics, as well as scientific, economic, social, and practical knowledge to invent, innovate, design, build, maintain, research, and improve structures, machines, tools, systems, components, materials, processes, solutions, and organizations.
If you don't allow that kind of restrictions, many modern bridges should be consider art by that logic because "while looking good and distinct" was one of their design goals.
Precisely. They are both art and engineering -- that's the point. Generally, the art aspect consists of the aesthetic restrictions you've placed on your engineering efforts.
restricting a machine to mechanical operations takes severe engineering effort - what you are doing is just playing with words. you can program to display a time on a watch running Python inside - but you probably would have to research for years before coming up with a reliable and usable mechanical watch - not to mention the advanced features at display here.
Developing a mechanical way of doing this from scratch is much more efficient than developing the entire stack of technology abstraction layers (from transistors to CPUs to computer engineering to LEDs to OSes to programming languages and runtimes, etc.) to achieve this digitally.
Some spinning weals, gears, and springs are much much much more efficient!