He seems to make it pretty clear: "You give me a place to send them, and when my students join they punch in the required credit card and then they’re done." This sounds like a more streamlined signup process than what his users currently go through, which involves signing up somewhere else, paying, and then receiving an email with a link enabling them to sign up (again) at slack.
> how it would actually benefit Slack
Again, fairly well spelled out: "I promote it, I do the hard work of being in there, and you get to skim your $6.67 or however much the plan costs off the top of the signups." So free promotion, somebody else drives user signups to your product.
Third, by my reading, the author is implying that this setup would be useful for many others who want to offer a good chat service for online learning, paid support, or a multitude of other reasons I can't think up. It sounds like a great idea to me.
Finally: you'll probably get more out of the internet by being more concerned about content than tone.