Almost, its a little backwards. What I would do is move the wordpress folder from the zip into your site root so you have:
- and all the rest.
Then go to http://www.example.com/wordpress and go through the Famous 5 minute wordpress install to set up your admin and database and all that.
Now, log into your admin and go to settings -> permalinks and choose whichever you like (you can change it later, just pick anything except the default. This will create the .htaccess file for you). Save the changes.
Go to Settings -> General and make the site address http://www.example.com while the wordpress address is example.com/wordpress
Save those changes.
Copy (NOT MOVE!) the index.php and .htaccess files from the WordPress directory into the root directory of your site (Blog address). The .htaccess file is invisible, so you may have to set your FTP client to show hidden files.
Open your root directory's index.php file in a text editor
Change the following and save the file. Change the line that says:
Now wordpress lives (invisibly) under /wordpress/ and the site works from example .com.
Now, open up /wordpress/wp-config.php and add
/* Multisite */
define( 'WP_ALLOW_MULTISITE', true );
Then when you login next, under tools you will have Network setup that will get you going.
A couple notes: you can only use subdirectory multisite like this:
http://www.example.com/site2 and so on
Always change the security keys in your wp-config file early on.
The folder doesn't have to be /wordpress/ it could be /im-just-that-awesome/ for all wordpress cares. Just make the appropriate changes in wp-config and your Settings->General tab.
Lemme know how it works for you.