Atom was specified as an RFC in late 2005, compared to the current version of RSS, 2.0, in September 2002, and specifically as a replacement for RSS. That would seem to qualify it to "supersede RSS as a content delivery mechanism".
The linked article specifically states that "These days people tend to use Facebook and Twitter as de facto RSS readers to monitor their favourite sites and subjects. Content providers also favour these channels as they make it easier for them to analyse and monitise their audience.". So there's your answer to "what else to use?": Facebook and Twitter.
Note that at this time, at least as I understand it (I don't even have a Google account, personally), it's only Google's RSS reader that is being discontinued. Of course, since it is web-based, you can't simply keep running the last released version locally indefinitely.