In an earlier version of this question, I confused the issue by using the word company instead of employer. Strictly speaking, the magazine is not a company, but I was considered an employee of the magazine, not the publishing house that owned it. I'm not italicizing my other employers. Before I had this job, however, I worked as a freelancer at a variety of magazines, and I list a few examples in italics as part of the description of my stint as a freelancer.
If you are looking for work in publishing, your resume should follow the style used by others in the profession.
The Wikipedia biography of Anna Wintour has a nice set of examples, but the staff biography pages of any major publisher should do just as well.
Resumes are special bodies of writing, and hence exempt from many of the style rules we associate with proper writing. Therefore, it is unlikely that anyone would criticize your decision to italicize or not italicize the name of a magazine. It's more important that you maintain a consistent style throughout the document. Inconsistency is a much greater transgression than a style choice about italics.
That said, I personally, would choose to follow the same citation rules as a bibliography for many of the same reasons. Presumably, a prospective employer will be seeking out your work, and the information contained in that bibliography would allow them to easily find an example of your work. Most style manuals call for italicization of the magazine name in a citation.
If your work is not of a creative nature, the point is moot. Do as you please.