Most small and medium digital agencies I know of use the word "developer" in that way, as someone who sets up and manages CMS for clients, usually also doing customizations using stock plug-ins and sometimes writing plug-ins themselves. Handling all from configuration files, code to looks, UI and even marketing and photo editing when needed. And I can even tell you of some other companies that use title developer for people who only configure Microsoft Sharepoint for their clients, even more in my country people who sell newly build apartments are also called developers. It is just a word, it is not a real problem here.

The problem here in my opinion are your missed expectations and how are you reacting to this situation. I could just tell you "yes, those people don't know what a developer is" but that will not help you grow.

Looking at the whole thing from my perspective you seem to be very disappointed that this company did not meet your expectations and perhaps that you did not meet theirs. It's just a job interview. It's OK. Sorry if they were unpleasant, but it was their choice and arguing what a true "developer" really is will not change the outcome. I understand that you are upset, but what good will come from arguing about agency, that "doesn't even have..." ? There is not really a right and wrong in this situation, just you and that company did not fit together, do not think about it as your failure or as them abusing some kind of universal rule. It may hurt you, because you care, but really it's just a minor annoyance. A mismatch.

In a smaller service business, like a design agency, it isn't uncommon for each manager to be more skilled than their direct reports.

Example... I am a DesignWizard. I have a lot of business leads, more than I can manage myself. I hire minions who can do some of what I can do, but I am still responsible for the quality of the work. The agency continues to grow, and I now have more business than me plus minions can handle. SuperMinion can do all of the design work I can do, so promote him/her to MinionManager. As DesignWizard, I am still on the hook for the quality and delivery of all design work, but I'm trusting MinionManager to actually complete the work. MinionManager is pretty good design work, including CMS stuff (Joomla, Wordpress, Drupal, etc.). If MinionManager didn't know all of those things, I'd often get sucked back into the technical work, reducing the amount of time I can spend selling and growing the business.

They confuse the meaning of "developer". For them its someone who can develop marketing and digital goods - using Photoshop.