It's not a question that comes up very often, but it has come up, including in my own brain. Knowing (i.e., being very familiar with or having experience in) a particular industry or market is helpful, sure. But is it required?
The short answer: no. It doesn't matter.
Generally speaking, what works on the web, well, just works. Industry is virtually irrelevant. Of course, I say virtually because having some knowledge is certainly helpful. I'm not convinced, however, that it's the design studio's job to know everything there is to know about any particular industry. That's where the client-designer relationship comes in.
The relationship between a client and a design studio shouldn't be a client-vendor relationship (which is more akin to master-slave, although that's quite extreme). No, the relationship should be more of a partnership – a collaboration where the client brings their industry and audience knowledge and expertise, and the design studio brings design, development, and in some cases, online marketing knowledge and expertise.
A big key here is that each side really needs to know their stuff. If the client knows their business and their audience, the design studio can apply that knowledge to the user experience, the visuals, and the overall solution.
That doesn't work, however, if neither party can communicate well with each other. The ability to communicate well with each other is the absolute most important thing.