No way to tell in mm's how much play there is. It's not a lot, but definitely enough that I could tell, and it struck me as odd. (and again, on the cheaper BB, the adapter slid on easily, but had no wiggle room.)
Also, I can't discern any movement now that it's installed (but you wouldn't really expect that, after the main body has been threaded in tightly. There could conceivably be some flex, but I wouldn't be able to detect any back-and-forth rattle.).
And, yes, I did install the main (right side) piece first, followed by the left-side sleeve (aka 'adapter"). But, I don;t own a torque wrench, say I've always done these by feel and sight.