“The compressed air is trapped in what is referred to as a hydraulic accumulator. Efficient enough.”
Now there is something I know a bit about. As a machinist and fabricator, I built and installed hydraulic accumulators into industrial machinery. They are a steel cylinder with a floating piston, with compressed air on one side, and hydraulic oil on the other. They don’t hold a great volume of compressed air and as I see it, would be useful mainly to give an underpowered car a quick boost in acceleration in heavy traffic. Such a device would not take you around the block!
Based on the size of the accumulator in the diagram, I agree that it doesn't appear to offer much in the way of distance. I'd guess a volume something less than 20 gallons (total).
Your perception that the point of the accumulator is to give acceleration is quite correct. The engine is sized for average power use, and the accumulator provides peak power well above the engine power. Wiki has a pretty good summary at Hybrid_vehicle.