The barrel of a 1911 moves up and down when the slides moves backward and forward. The barrel is linked to the frame through the "barrel link", the "barrel link pin" and the "slide stop", so there's 2 node where movement is possible. On the muzzle, it's linked to the slide through the barrel bushing. When the slide is backward, the barrel has to move on the 2 nodes since the barrel bushing is fixed. When the slide is forward, the barrel bushing is at the extremity of the barrel so it's tight. Mostly tight at least. Note that if for some reason it wasn't super ultra tight, the would mostly end up being imprecise, not dangerous.
Basically, if there wasn't any play at all when the slide is backward (and barrel up), it couldn't function the way it's supposed to. I don't know if 2mm is too much, not enough or just right, but those things are fire tested at the factory so if it's new "untested", then I wouldn't worry too much about safety.
As for how good a shooter it is, if it's your first gun and you're starting with a 45, the chances are pretty good that it shoots better than you do