Semantically, wouldn't one call a neanderthaler creating/perfecting a useful tool an engineer as well, even though science was not really used directly?
“Until very recently engineers learned from the sciences, but most of what they knew was craft. The crafts were so much more advanced than theoretical understanding that the engineers worked like artists. You know, you learned how to do it. Physics didn’t really get to contribute to engineering theory until fairly recently. In fact, when I got to MIT not that long ago in the 1950s, it was still largely an engineering school, and physics was taught as a service. But if engineers wanted to construct electric circuits or build a bridge and so on, you learned for the profession and you learned some physics – and it helped you, but now it’s changed.” (http://www.justresponse.net/chomsky_offers_advice.html)
Science is a social movement, with a history we can look at. Like many movements, there’s lots misleading written about it. Often going into religion, especially when groups try to claim its prestige for themselves. (We might include mainstream economics here, but hilariously many capitalist economists aim beyond science, closer to math. At least many Marxists "only" claimed to have Scientific Truths.)
Marx was probably using the German word "Wissenschaft"[1] which is not the same as modern empirical science, it's means something like structured knowledge and it includes branches of knowledge like history or literature that aren't called science in English.
I think people get hung up on the idea of applied science, since applying science is typically one of the best methods of engineering. Our ability to engineer things is dramatically improved by applying the knowledge, techniques, and processes provided by science. But it's not the only way.
I feel the article dances around what the fundamental purpose of engineering is - that is to create viable real-world objects by solving problems of constraints and tradeoffs. Nearly all meaningful engineering problems can be posed as a series of constraints and tradeoffs. Even if you were out trying to sharpen a stick into a spear, you're intuitively (and probably iteratively) solving the problem of constraints and tradeoffs.
When you set out the make the spear, you might not even know the full extent of the problem. You know that at a high level the spear (assume a throwing spear) must be long enough to be stable in flight, short enough to not be a burden, heavy enough to fly well and deliver energy on impact, light enough to throw, thin though to grip easily, but thick enough to not shatter on impact, pointy enough to inflict damage, but not too pointy for the point to be too fragile.
You now get to solve this problem. Sometimes as an engineer you might get the exact values of these constraints given to you, sometimes you have to go find them, and sometimes you wing it. You can use science (work from material properties, dynamics, deformation, biomechanics), you can use some 'direct empirical evidence' (screw around and guess and check =D ) and iterate through a bunch of spear designs, or some rules of thumbs that your uncle told you or a mix of all.
The most important thing is that you are managing trade-offs and constraints at some level.
Stone age people were smart, and they knew that things go down, some materials are harder than others and a pointing object hurts. Engineering is the process of using that to build a construction like Newgrange or a spear to hunt. Making use of your understanding of the world to take advantage of the medium.
Science just allows you to greatly increase the understanding of the world, in a more precise manner and at a faster pace. You learn properties of rocks (science) that can be used to infer newer materials, lighter and more resistant than others (engineering), or to predict with more precision star movements (science) and allow you better navigation through sea (engineering).