Discord isn't really a Slack competing product as much as it's a Teamspeak and Mumble competing product... or at least at the start.
Initially it was just easy to use VOIP with rich text chat channels. Now they've added in video calls and a video game store meaning they're more gunning for Steam and even less for Slack.
I do not see them as being Slack competing. They're too casually focused to be a threat in an enterprise environment.
Default Windows 10 comes with preinstalled video games, much less a store. Discord already has subscriptions, at some point I see them selling a version with enterprise features.
I wouldn't say they compete directly as one is obviously targeted at corporate and the other is targeted at gamers. But they are extremely similar and even the UI, while themed completely different, is extremely similar.
On the other hand I use Slack daily.