I recently removed the valve cover and oil pan to do a thorough inspection of my timing chain & guides (2012 328i). I had an issue detailed in another thread.
https://f30.bimmerpost.com/forums/sh...w+oil+pressure
The timing components had been replaced less than 20K miles earlier under a previous owner under warranty by a dealer. I did notice that the guides moved in line with the crankshaft (you mentioned side to side, so we may be talking about different movement...), as if they were designed to float on pins rather than be fastened securely to the block. I did not have any play other than the fwd and aft movement, and nothing was broken or worn. Just a sample of one car, hope this helps.
I am curious as to what a good service interval is for replacing that tensioner. It doesn't look to be a bad job, and its not a crazy expensive part. I would much rather replace the tensioner early on a schedule, than have the guides fail and be facing a TC replacement.