The new rules do not eliminate the contraceptive mandate. They simply make it easier for individuals or groups with religious or moral objections to the mandate to opt out. Thus, most insurance policies will continue to cover contraception. To quote from the  rule:

"These rules do not alter the discretion of the Health Resources and Services Administration (HRSA)...to maintain the guideline requiring contraceptive coverage where no such objection exists."

Lawsuits against the mandate have largely been successful, so there is little reason to continue to try to enforce it. The DP editorial made it sound as if the new rule would eliminate all contraceptive coverage, which it will not do.