I don't think it's reasonable to treat everyone you work with as your customer, but that's not what's being proposed.
IT's role is generally to support the organization. The organization is its customer. For the most part, it doesn't "work with," but it supports. In any organization, there's a complex network of who is a customer, who is a client, who is a peer, and so on.
There are places I'm not IT's customer, but they're the exception rather than the rule. If IT isn't providing a service I need, then that's a failure of IT. At the end of the day, the fallback is to purchase the same service elsewhere. If IT needs to know about that (e.g. for audits or security), it's fine to have a process for that (I report to IT, IT verifies what it wants to), but if that process becomes an unnecessary roadblock (IT doesn't want to compete for my business, rather than a core security issue), either people will circumvent that process or the business will take a hit.
The customer-provider networks vary on business. In some cases, engineering is the customer of marketing, and in some cases, the other way around. You have companies where marketing decides what to build based on customer conversations, and engineering builds it. In other cases, engineering decides what to build, and marketing sells it. And then you have all sorts of cases in between, from synergistic peer relationships to all sorts of balances where one drives but the other informs.
That doesn't change the gross organizational dysfunction being described in this article.