In the ProPublica article, the example of Loctite Liquid glue is used:
https://www.amazon.com/gp/offer-listing/B004Y960MU/ref=dp_ol...
The first listing is indeed from Amazon.com as the seller. It has the cheapest price at $5.97 with "FREE Shipping" if you have Prime. So I assume that without Prime, there is a cost for shipping.
The next listing is as the ProPublica article claims, from "TheHardwareCityCo", with a price of $6.75 with free shipping.
Assuming that that free shipping, unlike Prime, is unconditional, it is worth pointing out that TheHardwareCityCo offers a shipping date from "October 3-12". I'm assuming that you also don't get the return guarantees that you do from Amazon.com.
Furthermore, the massive markup cited in Quartz/ProPublica -- $1,400 extra for buying a basket of the 250 most popular products -- only applies if you decided to buy each item individually, as Amazon automatically gives you free shipping (Prime member or not) if you buy $50+ worth of items.
Not seeing the big problem here, to be honest. Frankly, I get annoyed when the default seller for an item is not Amazon, and I have to dig to find the listing that has Amazon as the seller. I have Prime, so that makes a big difference, but I prefer Amazon's reliability over spending time trying to figure out which third-party seller is the least shadiest.