I clearly brought up designing planes and bridges, I figured both were enough to demonstrate that my definition of engineering includes the structural, the mechanical, the electrical, etc.
The point is, the engineer who designs the plane only needs to know enough math to design said plane. The engineer who designs the bridge? The same. Theoretically, they're supposed to understand a great deal. Realistically, the degree to which technology automates the mundane task of calculation could very well mean that their daily application and actual understanding of mathematics is overestimated anywhere from slightly to greatly. This will be especially true as time goes on and the tools of the trade become even more advanced.
To design a web application that operates efficiently in terms of cost, response time, and required maintenance, along with a number of other variables, requires good software engineering. Once upon a time, this required strong mathematical aptitude. Now, it requires more of an understanding of the language used for the design of the application itself, an ability to justify why one approach should be faster through algorithm analysis and efficient testing, logical thinking, etc, it certainly doesn't require the mathematical aptitude to design your own cryptography protocol whenever you can simply use a library demonstrated to be safe and reliable, although an understanding of the underlying concepts of how said protocol works might be nice, if anything to understand why you shouldn't roll out your own.
It's not too far off to imagine a near future where the average functionally requires the same degree of mathematical aptitude as today's current web developer.