And you are absolutely right to feel that way.
First of all, in my opinion, it is your job to say “No. The marketing content will come later, now we will focus on…” whatever you feel like focusing. Because you are hired to get the website together and it is your job to pave the way.
Secondly, honestly, it doesn’t sound like this will be a “satisfied customer, great job” kind of story in the end. But it sounds like an opportunity to learn to make your customer think through what he/she did not plan to think through In this situation I would probably continue with even more questions. Cause I need that information to do my job, and they are the only source I can get that information from. So I would probably most of the time start just answering with questions to make them think and tell me everything I need to know.
Boss: "Put the marketing material together."
You: "So what do we market?"
Boss: "Well, product A"
You: "What do you want people to know about it?"
Boss: "Well that it is good?"
You: “In what way? What is the competitor advantage? Do you have patents? Why should people choose you?”
Once you start getting key information flowing in, you’ll be able to at least plan out the architecture of the website and go from that.
Another option is to spend an hour, gather different websites as references, come to your boss, offer these options, analyze the feedback and maybe come not from the side of “what he needs”, but rather from “what he doesn’t need”.
Hope it helps