Piston rings rely on an oil film to avoid metal-to-metal contact. If there is no oil, the piston ring will locally melt and seize to the cylinder wall. That's what happens when a normal engine is run without oil.
Also, piston rings rely on an oil film to complete the seal. The tiny oil film blocks the path for gases to escape past the piston ring.
And ... Piston rings rely on gas pressure from above to work its way in behind the piston ring and force it against the cylinder wall. The more gas pressure there is, the more pressure the piston ring pushes against the wall. The initial tension is only to roughly hold it in the right position to get this process started.
The friction due to side loading of the pistons is much lower than the friction due to the pressure needed to maintain proper piston ring seal. Many racing engines use only a single compression ring instead of two, to cut down on piston ring friction. BUT, low oil consumption and maintaining compression for good cold starting and maintaining low piston ring leak-down for lower emissions are not priorities in those applications.
AND ... Piston rings need a little bit of oil to help transfer heat. If you don't do that, something melts, and the engine goes boom.
Piston ring without oil = seized engine. If clearances are made exceptionally large and the speed is kept low in order to avoid seizure, metal-to-metal contact without lubrication = very quickly worn out.
Wankel rotary engine apex seals have a tough situation because they also have compression/combustion space on both sides of them. Look how long it took to develop Wankel engines that seal properly ... AND ... they are designed to deliberately use a small amount of oil, because the apex seals will not last long without it!