so, I'm playing on another machine now than I registered from. is it necessary to re-register the game?
No. If you patch the game, activation is required, though. If you update uisng SDC it's handled transparently with no extra effort needed on your part. If you install from a retail disc set without updating, you need not register or activate until such a time as you choose to patch up.
and, where can I download the actual patch without installing "StardockCentral"?
It does appear to have been removed from the downloads page (I'm not sure why). If you absolutely refuse to use SDC, you may be able to find it on third-party download sites. Though via SDC you will be able to get the very latest version beyond 1.4x, which contains a few additional fixes.
and the program checks my system for stardock games and reports to stardock. this fact alone meets the definition of "spyware"
AFAIK, SDC uses the registry keys created by the game itself to see if it is installed or not, and what version. It doesn't scan your entire system for our products and it doesn't tell the server anything about what's installed unless you choose to update (in which case it needs to know the version since patching is incremental). If you've registered the game, the server already has your serial and thus knows that you own the game anyway.
The only thing I'm aware of including any information aside from that you own the game, and your account details (which we already know) would be the activation, but that's required whether you use SDC or not.