I was just in the Philippines, tons of ads for Japanese motorcycle brands. In places where competition and usage for the product or service is high, there will be ads, and lots of it. You use motorcycles as an example, but it probably isn't a very good example.
Engineer doesn't "imply calculus and physics". Calculus and physics is not in the dictionary definition of engineer. In fact, the verb form of engineer is exactly what software, network and devops engineers do. When you say it doesn't mean anything, you must mean you, yourself, doesn't know what it means. ;)
I have a graduate degree in engineering, so I at least have some idea of what it means. Are sanitation engineers 'engineers'? They are according to your dictionary definition.
Edit to say: before I went back to school, I was a technician (no degree) who had the job title of 'engineer'. After I went to school I realized how different the worlds of the technician and engineer are. Not to say one is superior. Just very different.
Does it make you a better infantryman? No. Is the type of person that plays games probably better at figuring out different mechanics of the various systems in use by the military? Probably.
You can't generalize "soldier" into one MOS(military occupation). While the main goal of the military is to fight wars and conflicts, that requires many different skill sets and different job requirements.
