The entity that operates 614 Magazine, Lewis & Clark, is an Ohio LLC. However it appears to be owned by a Nevada corporation, 614 Media Group. The two principal owners of 614 Media Group appear to spend time in Ohio, which means they are likely subject to Ohio individual income taxes regardless of where they have incorporated their holding company.
An entity that does business in the state of Ohio is required to register with the Secretary of State, and is also required to file any applicable tax returns with the Ohio Department of Taxation, to the extent it has income earned in Ohio. In this case, those taxes are likely the commercial activity tax and the pass-through entity tax. Ohio does not have a corporation franchise tax, though it probably did at the time 614 Media Group was incorporated.
The rate on the CAT is .26% of gross receipts. The rate on the pass-through entity tax is 0% for corporate investors, and between 5% and 6.24% for individual investors depending on how they report, withhold and file. Those are not outrageous tax burdens by any standard, and almost all states have comparable taxes.
Corporations organize in Delaware because the internal affairs of a corporation are governed by the laws of the state in which it is incorporated. Delaware has the clearest and most predictable corporate laws and low taxes, to boot. As for Nevada, that may be just tax planning.
All that was a prelude to making three simple points: 1)There are lots of good reasons to incorporate in as state other than the state where your principal place of business is located. 2) Ohio business taxes are not all that burdensome compared to other states (e.g., New York or California). 3) 614 Magazine still has Ohio tax obligations to the extent it earns income in the state; it may just be reducing them by incorporating elsewhere, and there's nothing wrong with that.
Oh yeah, and an afterthought: the OP makes two unsubstantiated logical jumps: 1) that the journalism side of the business is necessarily guided by the business side; and 2) that anyone reads 614 Magazine for its hard-hitting journalism. Don't get me wrong, I like the magazine, but sheesh - you'd think we're talking about the NYT here.