A lot of times, that plastic cup is disintegrated and just the ball end of the shifter handle is left.......causing the slop that you feel in the shifter......you can see the plastic pieces laying in the trans in this pic.....
I usually replace the torn/broken rubber top plate that stays on the shifter handle when you remove the shifter......that part is nearly $40.00 though!
Believe it or not......to install that rubber "boot" on the shifter handle, you lube the hole in the rubber boot & the shifter handle, and slide it down the shifter, and over the wide portion of the shifter handle! After you cut the old rock hard rubber boot off of the shifter handle first, of course!