Mechanical design is something that completely baffles me and leaves me in awe. I can comprehend almost anything electronic/digital, but I just can't fathom how one would conceive of a complex mechanism (let alone package it in a compact form!), despite understanding the physical concepts behind them.
You would think that more people would put two and two together but what baffles me is the dissonance in people's minds of ancient civilizations - namely that they were oh so primitive, but at the same time there is this underlying current of, "how could they have possibly known this if they were so primitive?" with the discoveries we find that they have left behind - whether it be mechanical, architectural, agricultural, whatever.
I think over all they were not much worse off intellectually than we are, but they haven't yet discovered certain things - much as we have yet to discover certain things. For them, it was a mechanical age for a very long time and they've mastered that in much the same way that we are slowly beginning to master electronics and chemistry. We've had a very, very slow ascent towards electricity until it has become commonplace as it is today. I doubt the design of electrical components that we can easily plug in and out with a bit of molten lead/tin would, to them, be anything short of wizardry.
So don't be distraught by the otherness of it. It is quite a different way to look at problems that really tests our understanding of first principles of the natural world.