The attacking system is shooting a firehose of requests at the target system, but doesn't have to deal with handling any responses being sent back to the requesting systems.

Makes sense, thank you!

It's an advantage because you as a botnet client have made the server side do extra work. You sent two packets, one to request a new connection, and a second to immediately cancel the request. The server on the other hand sees a connection request and does some work like allocating memory and fetching the resource you requested. Once the server starts sending the response back to the client via the reverse proxy, the reverse proxy notices the request is no longer current and just drops the response on the floor. As a result, you made the server do some amount of work and you don't have to worry about saturating your internet connection. They call this a magnification attack because for the cost of two requests you made the server do some multiple of work.

You could add some smarts to the server or reverse proxy that delays starting work in case a cancellation request quickly arrives. This is probably part of the mitigation work they refer to in the article.