The files that I downloaded from the site you posted are still the same. Nothing changed there. I didn't overwrite them. I only overwrite the files of patch 1.16.1 after I installed the normal starcraft (without remastered). Then I took Remastered folder and pasted it starcraft game directory.
EDIT: Nevermind, I JUST managed to make it work. What I did was uninstall and delete everything, then recheck all the downloaded files for starcraft, then extract x86_64 files, then repair via Battle.net, then apply the LATEST ZLoaderx64.exe, then run ZClient again and authenticate, then run through