He clearly describes how he got access to their Slack instance, which required finding a way to receive an email at a @target-company.com email address. He did this by signing up for the target company's service using feedback@slack.com, in order to trick the company's support desk software into making the email from feedback@slack.com visible to him in the customer-facing support portal. The target company's helpdesk software thought the email confirming ownership of support@target-company.com was from the new user who just signed up with feedback@slack.com, so it made it visible to him in the user-facing support portal as a ticket he had opened. That let him access their Slack instance.
The question was: how was he able to read tickets created when an email was sent to support@target-company.com, such as a password reset email from Twitter. Just joining the company's Slack instance wouldn't let him read emails sent to support@target-company.com. And he says he was able to do that by getting access to their Zendesk instance.
Presumably he used the same process, but substituting ZenDesk for Slack. Or else he used a different method that he doesn't describe.