I have the zip file but I don't know to install it from a .zip file. Here are the contents of the extracted chrome-linux.zip file:
A .zip file is an archive, so you can't install it, but can unzip or extract it - right click, select 'Extract here'. Call it installation if you like, but that's pretty much it. If you prefer the terminal way, then:
unzip chrome-linux.zip -d /destination_dir
To run it
cd to the installation directory, and then run
Needless to say, I'd strongly discourage using any unofficial version of Chrome. It could be unsafe, and your best bet is to get the real thing instead.
I could not find a zipped version of chrome to test this, but my guess is that you need to put the chrome-linux directory somewhere like /opt, and then set up a lanucher to point at /opt/chrome-linux/chrome. If you want to be able to execute chrome at any time from the command line, you might also put the chrome-linux directory in your path. Just put
at the end of your .bashrc file in your home directory.
That said, if all you're wanting to do is install the stable version of chrome, then you probably want to go to http://www.google.com/chrome and download the .deb file instead.
You seem to have downloaded the build of chromium, in order to run that as mikewhatever suggested, all you have to do is to extract it and run the chrome binary, no installing is needed.
You can also add a launcher to ubuntu which runs the binary for you, which means you can just double click to launch. To do this right click on desktop -> add laucher -> In command, enter the full path to the chrome binary.