If the handle screw is tight and the slop is below that then look closely at the shift mechanism for any breaks or cracks. It's cast aluminum and if someone is really rough with it, it can and will break. This usually happens when the BTSI (brake-to-shift interlock) solenoid, or the brake switch goes bad, and won't let you shift out of park, then frustrated owner starts reefing on the shifter until the mechanism breaks.
You can get that mechanism brand new for about $100-$125, Dorman 905-101. Dorman's quality can be sketchy and I don't know if that particular item from them is any good. There's also knockoffs of that from those made-up-name companies you see on amazon. The real GM part will set you back about $200.
Richard