It doesn't NEED a stop ring for the agitator, but in cases where there is a little too much play in the agitator, I've used a stop ring in addition to the set screw.
Since you have it partially disassembled, now is the time to check a weak spot before it gets ugly. I would pull the spin tub and check that boot seal under the tub drive block. If it's clean with no signs of rust, put back together and call it good. If there is ANY sign of rust or water contamination, I'd think about replacing the mounting stem/boot BEFORE it gets bad enough to warrant pulling the outer tub and doing a tub bearing job. This will be a small investment now in a machine you'll have for a LONG time. Congrats on the find! A A9900 set has always been on my short list of wishes!
RCD