That is a remote reservoir for the shock fluid. There is a piston inside that separates the fluid from the high pressure gas (usually nitrogen). This stabilizes the shock action as it heats and cools, note that the exhausts are pretty close to the shock body. Simple shocks tend to be emulsion type, where there is no separator.
The cylinder that pushes fluid into the preload adjuster is under the black knob. I don't have much to complain about the Sachs shock, we'll see how it feels after I get my forks back. But I can order an Ohlins that offers the same, plus compression adjustment. When it comes to suspension parts, you generally get what you pay for. Ohlins is the gold standard of the industry, with Showa close behind.
PS I don't have the parts list handy, but I suspect that the regular Hypermotard uses the same shock - maybe without hydraulic preload.