Well, I reinstalled the K-Lite and K-Lite 64 codec packs. I left everything at default (meaning TrueMotion decoder is set to libavcodec) and... everything works. I'm still completely confused, but at least the game works.
So, I guess, uninstall all codec packs, install FF7, install the movie player from the CD, reinstall the codec packs, install 1.02, and all is well in XP64....
... for now.
Thanks for all the help!