They rotate. If they didn’t why pin them?
I’ve been building engines for long time and also own an operate an engine dyno. The only rings that are pinned are in two stroke engines and that is to keep the ring ends from rotating into a port and breaking off.
So you will properly space the end gaps in the rings and not stack them on top of each other. The end gaps need to be properly spaced apart. If they weren't, you would get a vertical ridge in the cylinder wall where no rings ever contacted.
I’ve been building engines for long time and also own an operate an engine dyno. The only rings that are pinned are in two stroke engines and that is to keep the ring ends from rotating into a port and breaking off.
That is only one reason. The other reason is to keep the end-gaps equally spaced apart for the reason I stated above. Rings don't spin around in the ring lands. I've built and re-built a host of different engine configurations for decades. Unless the rings are pinned in the ring lands, I install the rings with the gaps at 4, 8, and 12 o'clock positions. I've torn down the same engines years later and the rings never noticeably moved from when I originally installed them. The cross hatch hone pattern originally installed in the cylinder walls wears away during engine break-in when the rings seat. It does not exist to make the rings "spin" around the piston.