Is the takeaway that the increase in C-Reactive Protein, in those who eat more calories at night, happens due to the stomach's processing of food increasing the chance of interrupting the sleep-wake cycle?

I don't think there is sufficient information to draw the conclusion that only the only contributing factor is the disruption in the sleep wake cycle. It is however possible that is a contributing factor.

Which could mean that anything that disturbs your sleep-wake cycle has the same effects?

I think more research looking into this specifically would be necessary.