If the shifter lugs are worn then yes it is going to seem really loose.
Worn lugs are really common on these old transmissions


1953 Chevrolet 3100
261 cu inch, sm420, 3.55 rear, torque tube still,omaha orange, still 6 volt, RPO green glass, side carrier spare, all done
In the DITY Gallery
Video of the 261 running

1964 GMC 1000
305 Big Block V6, sm420, the next cab off restoration