When a journal requires that the work has not been published before except as a "preprint", is an arXiv publication considered a preprint?
Usually depositing a paper in arXiv prior to journal submission does count as a preprint. Wikipedia explicitly says so...here's the wiki link: https://en.wikipedia.org/wiki/ArXiv.

You can check out this list of journals with preprint policy: https://en.wikipedia.org/wiki/List_of_academic_journals_by_preprint_policy
If you posted your paper in arXiv before submitting to the journal, do inform the journal (include the link to your paper in arXiv). From your post, it seems that your journal does not have such a tight preprint policy.