Good question.
There is a comment above suggesting containment of solidified gas (CO2) warmed to a gaseous phase change for the required pressure. But in the world environment of ambient temperature and pressure it would require big energy to separate and liquify the gas in the first place. Thermodynamically there would be no way to invoke that as an overall efficient driving mechanism. One is just displacing the required energy from the auto itself to the solidification site (even if it is onboard).
Your chemical reaction thought is scientifically deeper. The chemical reaction itself is controlled by the temperature and pressure under which it occurs, so as the overpressure and temperature change with the contained reaction so does its mass balance. There is such a thing as chemical potential, fugacity, peculiar to the individual reagents involved, so I think an analysis could be done depending on the reactants and the containment configuration.
It doesn't strike me at first that there is any fundamental thermodynamic reason (three laws) that there could not be a given reaction producing like what you are thinking. Of course it would also depend on the availability, volatility, artefact, conditions, etc. of the reactants wrt their origin.
But the big thing is if it were a clear case of intrinsically available reactants than the process would have been exploited anyway over the last few hundred years of industrial revolution.
The one profound aspect of this auto article is that pressure is every bit an accessible form of energy as heat. Pressure is energy per unit volume, so that available pressure difference, like between the ocean floor and the atmosphere, or between the containment and release chambers of this auto, is a viable source for human (negentropy) use. It's just a matter of getting the pressure difference in the first place,e.g. ICE.
Anyway, nice question, hopefully there will be other insights.
I like your answer to the chemical question far better than my attempt a humor answer. I have question for you: As you say, there is a pressure difference between the top of the ocean and the floor(depending on depth of course). Would there be a feasible way to use that pressure to build pressure in tanks and use it for energy converstion, for instance a deep water electricity generating plant?