i don't know of any mopeds that don't need rings. you NEED rings on that piston. both of them. if you only have half a ring, do look very closely at the cylinder. if it's scored, you broke a ring somewhere and you can write that clinder (and probably also the piston) as a loss. if that's the case, you may want to be very careful w/ the engine. if pieces of piston rings went inside the engine itself, you may be in deep trouble.
call handybikes, or check online for piston rings. you may end up needing a whole tope end. do not even try to start that moped until you have rings on that piston. you will ruin your bike.
also, be sure to specify what kind of moped and engine you have. not all mopeds are the same. they have different size pistons and rings and cylinder and everything else. be very specific.
but, yes, to keep emphasizing what everyone else has said: you need rings on that piston.