Sort of right, I think
Unfortunately no, as the version of Mac OS X on those disk is older than the OS version the Mac mini came with.
You either need to get replacement disk or the Snow Leopard 10.6.3 Upgrade DVD or simply clone a working 10.6.3/4/5 Mac to that Mac mini in Target Disk Mode and run Software Update afterwards when booted from the Mac mini.
I think that this is slightly misleading....... I don't think the POINT version is relevant. So long as the base OS is correct, i.e. in this case Snow Leopard, then on the first software update, any appropriate hardware updates will be performed. I have a 15" Unibody MacBook Pro, around 6 months old. I purchased it second hand, had SL on it, but put a 1TB internal HDD in it, so required a re-install. My Original Snow Leopard DVD (purchased on Launch day) installed the machine with no problems....... your mileage may vary, but as Apple with their OS's, unlike MS with Windows, do not have install codes, if it does not work (and I am sure it will), you will only have lost half an hour of your time !
Good luck, let me know how it goes.