The white paper is only the overview of the underlying system. You're not going to find anything about the marketplace (look that up, it's funny), payment systems or other applications of Bitcoin in there.
That's why I mentioned the wiki. Like all wikis it's bit rotten and outdated, but it contains a lot of good pointers to the source material, both code and discussions. The page about "Payment channels" isn't a bad first guess. It is too old to help you understand modern systems like Lightning, but it will contain pointers to several other payment channels that have been proposed. Including Nakamoto fast transactions, which as the name might suggest was suggested by Satoshi. It turned out to be a flawed design, but the underlying ideas are basically the same as today.
As an interesting side note, that design was based on replaceable transactions. Another popular thing to copy paste into Bitcoin discussions is some conspiracy why this was developed (and it was indeed proposed for removal in the altcoin chain released today), but here you can see it was actually in Bitcoin from the beginning and how it was supposed to work.
You will also note that many other developers were sceptical about payment channels and preferred instead to work on sidechains, ecash bonds, and other methods. It's not like Poon and Dryja worked in a vacuum, but their work looks like it could actually be useful. Personally I don't expect it to be the final design for payment channels, and there are still much work to do on other methods of zero-confirmation high-throughput payment networks for Bitcoin (such as the above mentioned).
There's still a tremendous amount of work on the technical side of Bitcoin almost every day. Much of it just isn't end user visible because people are still laying the ground work for things to come. We're still very early. This is probably also the reason why these types of work doesn't stir up so much discussion on the mailing list. People are not going to re-base their ongoing work to some other codebase just because someone on Twitter threw a tantrum.