Power Cylinder
A bad power cylinder should not cause play in the steering. If it is very weak, it may keep the power assist from coming in strong, but there shouldn't be any play.
Other than the obvious checking for leaks at the rod seals and hose fittings, the way to check if the cylinder itself is in good shape is to disconnect the hoses from the cylinder, remove the rod end from the frame, move the rod in and out of the cylinder, and pump all the fluid out.
Cover both hose ports with your finger tips, then try to pull the rod in and out. On a good cylinder, you should feel strong suction on your fingers and the rod should barely move. A fair cylinder will let the rod go in and out a bit, but very slowly with the ports closed off. If the rod moves in and out with little resistance,then the piston inside the cylinder is worn and the cylinder will have to be replaced. It is a welded and sealed unit, so this can't be easily repaired.
If you have to get a replacement, try for a quality rebuilt original. If not, get the new repro from Stainless Steel Brakes. Don't recommend the other USA made repro. Don't bother with the Flaming River import.