North Carolina law defines the word "business" in "business pursuit" as "an individual's paramount means of earning a livelihood." North Carolina Farm Bureau Mut. Ins. Co. v Briley, 491 S.E.2d 656, 659 (N.C. App. 1997). CMLP has identified no New York cases interpreting this test in the context of online publishing out of the home (or elsewhere). As a general matter, however, North Carolina courts have declined to include part-time work under the exclusion, at least where the insured also had a separate full-time job.
Therefore, if you live in North Carolina, then you may have a good argument that your online publishing activities are not a business pursuit so long as they do not constitute your primary occupation or source of income.
Note that specific language in a policy might lead a court to a result different from the overall state trend.