Ok, here's the thing about Mac and application installations.
Often, all the installer does is create a folder somewhere in your Library for the application (and sometimes it doesn't), and moves the application to the Applications folder. Sometimes more in-depth applications create folders in other areas of the Library, and sometimes populate them with files, but for the most part, they are self-contained, unlike many .exes, which will give you an error if you remove a file from some obscure folder. If you can, install Chrome on another Mac, or find an already-installed copy somewhere, and simply put it somewhere on the hard drive. That should work.