I asked Alex Twersky, resume revamper for mb, about what programs writers should demonstrate that they know on the resume when they apply for gigs (other than Word). However, he misunderstood my question, but in rather a helpful way:

There is a very simple answer to that: no matter whether you're a designer or editor or a cross in-between, the global standard word processing program is MS Word. I advise against formatting your resume in anything other than Word because most hiring managers still use it to review resumes. For designers, I recommend saving the fancy design for your portfolios, but keeping your resume in Word.

Then I asked him again and he cleared up my first question:

A writer should definitely know Word but I think other important skills to demonstrate/know are style guidelines (i.e. AP) and clear editing skills, including copyediting, proofreading and layout.

So while you might not need to take a class in Quark to put on your resume, at least pick up a copy of the AP Style Manual so that when you're given an editing test, you look like you know what you're doing.