So if this engine changes the compression ratio (the amount the mixture is compressed) how is all this complexity better than a supercharger which changes the a

So if this engine changes the compression ratio (the amount the mixture is compressed) how is all this complexity better than a supercharger which changes the amount the air is compressed? Surely increasing the compression of the mixture and compressing the air before it goes in is pretty much the same thing? Except...that all that variable stroke length mechanism is a lot more complicated, and patentable?