I can imagine an extremely long term significant effect of this is that, assuming we remain confined to our solar system, there's gonna be not only global warming but a systemic overheating issue, namely because to carry up the increasing demand we'll get an increasing spontaneous energy output, and losing that energy from our environment gets tough after a while as we begin to run out of things to sink heat into.
A way to divert this:
Regulate the amount of these things running based on the long term projection of heat re-radiating out into space as a result of black-body radiation.
Or, maybe in the cataclysmically nearsighted scenario, maybe someone could do something with laser cooling to vent high-heat into interstellar medium. Maybe.
Looking in the much shorter term, logistics for belligerent elements suddenly got a lot more viable.
One possible circumstance I can imagine is... Uh...
Well I was trying to find out lists of underground facilities specific to their atmospheric volume and getting nothing. What I was trying to postulate that someone running a self-powered hydrogen producing electrolysis system in a particularly voluminous but relatively airtight underground facility for a long duration of time could lead to at least locally catastrophic effects if it is both vented and ignited...
But I can't even make ballpark estimations on the total exothermic energy release of the burning of hydrogen at those conditions, so the point is mostly conjecture at this point. Either way, the point is that things requiring power may not always have very viable paper trail-blazing behind it, in the worrying case that someone innovatively comes up with a way to utilize it for a large scale means.
Also, before everyone starts bringing up the statements of outright suppressing it, it may be a little more complicated than that. Why? Because the US military industrial complex. Specifically stating, having self-powered machinery would be an unbelievable and immense innovation that the military could not skip out on, mainly because, predictably, other nations will adopt it as well.
I foresee an integration in world military and economy, and a vaaaaast increase in international tension before anything could be expected to be even semi-permanently positive coming out of it.
On top of things, the food market in countries which have yet have fully integrated machinery in their agriculture will crash, as transporting food and even harvesting it will be relatively trivial compared to how it is IRL, with transport and harvesting no longer needing fuel. But on top of that, foreign aid groups and charities will be similarly empowered by this development which is simply un-suppressible beyond flimsy regulations at this point, so the overall change of living conditions in such countries are unpredictable, but likely positive in at least the short term.
Regarding the "Oil Barons" themselves, their lasting power depends on public reaction. If the sensation balloons up rapidly enough, the possibility of their stocks crashing is definitely worth considering, but they will still have some existing purpose, particularly in the manufacturing of polymers from oil until the sheer availability of power allows us to manufacture polymers "from scratch".