|Some interviewers ask for a write-up to see how carefully an applicant has been paying attention, not realizing that such a request often causes applicants to pay attention to other companies.|
If you are interviewing for a job that requires you to observe situations without taking notes and write them up afterwards, this might be an appropriate and job-related request. Used in this way, it would be a work sample. However, this does not sound like something one would be doing in a marketing job.
Another flaw inherent in this request is that an applicant should be doing most of the talking in a job interview, and everything you talk about should be job related. As a result, one could half-seriously argue that you should just resend your resume to him. And since it is so important for an interviewer to listen to an applicant, perhaps your interviewer should be the one who writes the summary.
It is not difficult to determine if an applicant is paying attention, and the best way to do so is by asking follow-up questions. Giving job applicants petty assignments only makes a company look petty.