Philosophy major here. Didn't read the article, but will point out:
The significance of Gettier problems as we investigated it is the exposure of an entirely _wrong_ mode of philosophy: philosophizing by intuition. Ultimately, the reason Gettier problems are significant is because for philosophers, the textbook Gettier problem works because _for philosophers_ the problem captures their intuitions of knowledge, and then proves the case of knowledge fails.
Most normal people (i.e., not philosophers) do not have the same intuitions.
After Gettier analytical philosophers spent decades trying to construct a definition for knowledge that revolved around capturing their intuitions for it. Two examples are [The Coherence Theory of Knowledge][0] and [The Causal Theory of Knowldege][1]. Ultimately nearly all of them were susceptible to Gettier-like problems. The process could be likened (probably) to Goedel's Incompleteness proof. They could not construct a complete definition of knowledge for which there did not exist a gettier-like problem.
Eventually, more [Pragmatic][2] and [Experimental][3] philosophers decided to call the Analytical philosophers bluff: [they investigated if the typical philosopher's intuition about knowledge holds true across cultures][4]. The answer turned out to be: most certainly not.
More pragmatic epistemology cashes out the implicit intuition and just asks: what is knowledge to us, how useful is the idea, etc. etc. There's also a whole field studying folk epistemology now.
[0]: http://www.oxfordscholarship.com/view/10.1093/acprof:oso/978...
[1]: https://en.wikipedia.org/wiki/A_Causal_Theory_of_Knowing
[2]: https://en.wikipedia.org/wiki/Pragmatism
[3]: https://en.wikipedia.org/wiki/Experimental_philosophy
[4]: https://en.wikipedia.org/wiki/Experimental_philosophy#Episte...