As mentioned in the article, using atomic swaps, a user can trade directly with another person. Using software that facilitates the trade (as these Dexes do) is not considered a third party. Throughout the entire process from fiat to Bitcoin, you do not need to trust your counterpart or an escrow. No reputation system needed.
Newbies may not want to do this but it is good for the community that this option is out there.
Wait, if anything is being used as a "medium of contact", how can't it be said as a third party involvement to settle things between two counterparties based on the data of the conversation that these third party apps have over cloud? And how will this atomic swap actually take place without the involvement of a software/app? Isn't that software itself considered to be a third party software that possesses the details of the transactions? Is this atomic swap some sort of a virtual box having two equal sides, one of which will take crypto in it and the other will take Fiat and swap immediately once both the equated amounts are filled in?