What is the importance of Copywriting skills in article marketing?

I agree that some copywriting skills are applicable, in part, to writing article titles. But there are also SEO considerations in titles, such as the importance of having your major keyword at the start of the title. SEO considerations and copywriting considerations don't sit too comfortably together.

Other than that, the extent to which copywriting skills are relevant, rather than just "article writing skills", in general, and particularly with reference to the resource-box, depends on what model of "article marketing" one's using.

I see that people who are "writing for clicks" will perhaps value slightly more than others a "copywriting approach" to resource-boxes, but that isn't my idea of article marketing at all. I think "writing for clicks" is actually aiming only at fast traffic, and is often positively shooting yourself in the foot with regard to syndication, which is where the real money is, in article marketing.

I've done enough professional copywriting myself to be aware of the importance of avoiding it, really.

No, I don't really. But in any case, if you'll excuse the observation, I think you're asking that question with a "writing for clicks" hat on, and that's not something I'd ever wear at all for article marketing, myself. And I think the Hawaiian cat above has the right idea, too.

Exactly right. Title your article "3 Ways To Skin A Cat" - then tell the reader early on that there are really 5 ways and they really should know them all. Then go on to give the 3 you promised in the title. End your article with a teaser to get the full picture (the other 2 critical ways) by visiting your site.