Calling them "worthless" is possibly an overstatement and certainly designed to grab the reader's attention. I would argue the former and I would say that the latter is within my purview for making the article worth reading.
As far as perimeter firewalls being worthless...
In the late 90s I was the director of engineering for Checkpoint's #1 reseller on the west coast. We received numerous awards from Checkpoint. At it's height we were installing a pair of HA perimeter firewalls twice a week and then managing those firewalls under a managed service agreement. We managed several hundred firewalls month to month. I was the principle architect and creator of this product and service.
In my experience, most of the firewalls that I put in could be relatively easily subverted because the firewall rules did very simple port-based filtering. An attacker could breach a system via this port and then use the "pinholes" (e.g. port 80, 443, or UDP on 53) to expand access. This approach to restricting port access to a set of pinholes is as useful as a deadlock on the front door of your home. It will keep the casual intruder from entering, but for anyone serious, it's little more than a diversion at best. Given the level of state sponsorship in today's world, perimeter firewalls are "worthless" in my opinion.
Sure, you need them because they provide the basic front door lock, but for the majority of cases that are most important they may in fact provide a false sense of security, which is dangerous. Perhaps worse, is that the perimeter is really difficult to define and therefor hard to truly secure. One might even go so far as to claim the perimeter doesn't exist.
I talked about this as far back as 2003 in my first attempt at blogging that was security focused:
Today, with BYOD the problem is much worse. Sure, perimeter firewalls are necessary, but at this point it's shocking how much reliance is *still* put on them when even in 1999 it was fairly apparent they had a very limited utility. Defense-in-depth is still a key watchphrase, and I think de-perimeterization of security should be another one. I don't think virtual firewalls are necessarily a help either.