Q: I want to see if this distributor play is unacceptable in this video https://www.youtube.com/watch?v=E-CihAjlSUE

I am replacing my distributor cap and rotor. I want to find out if my distributor needs to be replaced or not as well. The video I posted is not mine. It is of a similar car with nearly the exact same play. When I push the rotor forward and backward it does not move at all, however, it does rotate. It moves up and down too. I measured it with a depth gauge and the vertical play is just slightly under 1 mm. I know the distributor has to have some play in it or it is bad. However I also know too much play can also be a bad thing. In the comments section of the video one person said the distributor was bad. No one responded to the video saying the play was an acceptable amount of play. So, my question is how do I test the distributor to make sure it is still functioning 100%? And, is the distributor in the video I linked a bad distributor?

My car has 18900 miles.
My car has an automatic transmission.