From you description, it sounds like it only needs some minor adjustment. The left or non drive side of the bottom bracket which is shown in the photo is the adjustable cup. These are always right hand (normal) thread, and this is the only side you touch for adjustment.
You'll need a lock ring wrench and some sort of wrench to grab the inner flats of the adjustable cup itself. The lock ring wrench is more important.
Loosen the lock ring. Tighten the adjustable cup a tiny bit, say an 1/8 turn or less. Re tighten the lock ring. Test for play. When you tighten down the lock ring, it will affect the tightness of the bearing. For this reason you have to keep repeating this process. Fiddle with the position of the adjustable cup slightly, and retighten the lock ring again, until the bearing is as loose as possible but with no play. It might take you three tries. It might take 10.
All adjustable bearings on old bikes are like this, so it's a basic skill for C&V.
It's helpful to have a proper BB wrench that fits the flats of the adjustable cup to hold it in place when you tighten the lockring, but you can get away without it. It just takes more cut and try.