He seems to be saying that it doesn't really solve any of the "problems" of e-mail, because once everyone you know starts using it, you have exactly the same problem of keep up with the Slack messages as you did with keeping up with e-mail.
The main "advantage" of Slack is that it's used by far fewer people than e-mail, so fewer people can send messages to you. That advantage disappears though once enough people use Slack. The same thing applies to any other alternative messaging system.
The real problem isn't the method of delivery. The problem is that lowering the "cost" of communication means that you get a lot more communication. What e-mail did was give us ultra-low cost of producing messages. Basic economics says that lowering the cost of production will result in more being produced. The only way Slack will do anything about the volume of messages is if it is so hard and expensive to use that nobody wants to use it except when absolutely forced to.
What's needed isn't another proprietary message protocol, or just tossing some "cloud" in to the mix. What's needed is to automate the "reading" of messages so that you don't have to look at them unless they really matter to you. In other words, we need software that can somehow act as an automated personal secretary who can process and "understand" the incoming messages, and then use that to give you only exactly the information you need when you need it (and wipe your chin and tell you to brush your hair, etc.).
When that day comes, then my "virtual secretary" will contact your "virtual secretary" and they'll sort out everything between them and let us know what they've decided we ought to do. Until then though, we're stuck with sorting out the crap ourselves.