I think Nissan calling it “the world’s first variable compression ratio” engine is a bit of hyperbole myself. Haven’t variable compression ratio engines been used for years to test the octane rating of fuels in laboratories?
Both supercharging and variable compression can add power , but variable compression increases fuel economy and supercharging hurts it.
I can see it increasing part throttle fuel economy but since the compression ratio would be at its lowest during full throttle, I don’t see exactly how it would increase power, except perhaps to allow engines that normally run in an atkinson cycle to decompress enough to allow otto cycle operation during maximum power.
Supercharging doesn’t always reduce fuel economy. Crank driven superchargers have bypasses for part throttle so they only have frictional losses and added to smaller engines in larger cars, improve fuel economy. The SC loafs until the extra power is needed, then the bypass closes and boost builds.
Same thing for exhaust driven turbo chargers.
Ford has had that on their DOHC 4-valve V8 engines since they were introduced in 2011. 4 cam phasers on 4 cams on two banks of a V8. And they certainly aren’t alone nor were they the first to do that.
Even when the supercharger is working, a part of the energy used to compress the incoming air is recovered during the engine’s intake stroke. That’s a big reason why turbocharging actually makes a diesel engine more efficient. The air is never throttled so the intake stroke becomes a second power stroke as the compressed air in the manifold drives the piston down as it fills the cylinder during the intake stroke.