In the case of r/LoL it's replaced TeamSpeak, and for quite a few other communities it's replaced IRC or other chat systems, but a lot of subreddits and old school forums have been replaced with Discord servers too.
For instance, many speedrunning communities are now primarily focused around Discord servers, as are communities for the Mario RPGs, the Luigi's Mansion series and most game mods/fan projects. An awful lot of communities focused around YouTube and Twitch personalities have made that jump too.
So while the article may have not given the best example, there are definitely a lot of instances where Discord has replaced, or at least significantly hurt the activity of a subreddit.
It used to be that any decently organized guild would have a private voice server (be it Mumble, TS3, or Ventrilo) and a forum. The first was for event communications and the second for organizing events (calendar, recruitment, roster management, documenting strategies, etc). Now, all of that happens in Discord and very few guilds seem to have a dedicated website much less an operable forum.
In FFXIV specifically there is a virtual item called the 'Linkshell' that lets you join a private chat channel in-game. The only problem is that you are limited to the number of Linkshells you can hold, each Linkshell has a cap of 64 members, and you have to be in-game to talk to them. At some point in their early stages, Discord offered an integration with one of the FFXIV databases and it displaced the linkshell communities seemingly overnight.