Does the FAA consider flights that generate content for profitable YouTube channels displaying airborne video to be commercial operations?
The answer here is, potentially yes, but it depends.  In the United States the Federal Aviation Administration casts a wide net out over all kinds of activity it sees a potentially commercial in nature.  Former FAA lawyer Kathy Yodice wrote an AOPA article on what the FAA considers compensation or hire activity.  Unfortunately, the answer is not always clear; the FAA sees compensation as virtually anything of value and often just “knows it when they see it”.  Yodice writes:

Certainly, compensation comes in the form of any payment of money, but it also includes those instances when no money is made on the flight or when the payment isn’t even enough to cover all of the expenses.  The simple exchange of money to reimburse all or some of the expenses like fuel, transportation, lodging, or meals is usually enough. Compensation can also take the form of accumulation of flight time. Compensation can be good will or the expectation of future business. It could be the effect of furthering one’s economic interest or the prospect of a return favor. Something of value paid or given to a third party could be considered compensation if it is conditioned on the operation of the aircraft. For now, the FAA’s policy is to draw the line at considering charitable deductions of costs as compensation:  “Since Congress has specifically provided for the tax deductibility of some costs of charitable acts, FAA will not treat charitable deductions of such costs, standing alone, as constituting ‘compensation or hire’ for purposes of the regulations.” But, that is about the only exception we’ve seen in practice.  Otherwise, if you get something for taking the flight, the FAA is likely to call it compensation; if, in fact, you get nothing, you won’t have run afoul of the regulations.

So could a private pilot run afoul for making money on YouTube for flying videos?  Possibly.  Essentially YouTube is brokering an arrangement between content creators and advertisers and videos are ‘something of value’ to advertisers.
But here’s the catch.  In the above scenario, you are not directly exchanging your ability to pilot an aircraft for something of value; you’re simply out flying an aircraft.  Recording the flight is just incidental to it.  Editing, publishing and then selling the footage for compensation is something you’re doing on your own time and not related to your flying.
Another caveat is that §61.113(b) states that a private pilot may act as PIC for compensation or hire if:

(1) The flight is only incidental to that business or employment; and
(2) The aircraft does not carry passengers or property for compensation or hire.

Now in the YouTube scenario, a professional content creator’s business is content creation, not flying and the flight was only incidental to the person’s primary business.  It’s similar to an FBO employee and private pilot asked any his supervisor to ferry an airplane from the main office to a satellite airport for use there by the business.  Here the employee, even though a private pilot, many fly for compensation or hire as the flight was only incidental to the business.
Now let’s take a scenario where, say a content creator and private pilot gets numerous requests from social media subscribers to shoot a particular location from the air or the performance of specific maneuvers or demonstrations of the aircraft.  In this case we begin to get into a gray area where the overlap of exchanging airmanship for something of value starts happening.  It becomes even more suspect if the persons making the request are authorized representatives of the firms which advertise on this pilot’s social media channel.  Potentially an overzealous FAA inspector could cite you for flying for compensation or hire.
Again it all depends.  For more information on this subject I would consult an attorney who operates specifically in aviation law.