Erm, I'm not sure I get it. I think I'd need to see an animation. If the crankshaft is fixed I don't see how that linkage can change the stroke length because all it shows in that diagram is the piston further along the stroke, which is what all piston engines do when the crankshaft rotates.
So yeah, I probably need to see an animation to grok it.
The crankshaft is in the middle part it doesn't move in relation to the head.
The image explains is pretty well, the piston is connected to the "multi-link" which changes the angle make the piston head move further into the cylinder.
The compression ratio changes because the mechanism changes where TDC (Top Dead Centre) is.
Or have I misunderstood something?
Edited to add: If TDC moves then the bottom of the stroke moves with it because the conrod is a fixed length, right?