You don't give many clues about which version you are trying to download, I'm guessing it might be the Linux jar files? I've just downloaded that and it includes 5 jar files and a readme.txt, as it should.
The windows version is an exe file, wizardinstallv4.11.exe. I've just downloaded that as well, it downloaded correctly. What is in the readme file you are seeing? Maybe something you are using is blocking the exe file from being downloaded?
So you downloaded the file, ran it, did the install, and at the end you are seeing the web page about REW? If so, that is exactly what should happen. REW has been installed and is ready to run. The web page is shown on completing the install.
Run it the same way you ran it on your old laptop, double click the REW icon on the desktop or go to the room eq wizard entry in the programs list. Are you perhaps running Windows 8 for the first time and suffering from not having a start menu? On Windows 8 there will also be a tile for Room EQ Wizard in the Start screen. If you are on Windows 8 or 8.1 and would like to restore a Start button go to http://classicshell.net/.