Welcome to Apple Support Communities.
You didn't read quite far enough on the apple.com page you linked to:
"About the Family Pack
The Family Pack Software License Agreement allows you to install and use one copy of the Apple software on up to a maximum of five (5) Apple-labelled computers at a time as long as those computers are located in the same household and used by persons who occupy that household. By 'household' we mean a person or persons who share the same housing unit such as a home, apartment, mobile home, or condominium, including students who are primary residents of that household but reside at a separate on-campus location. This licence does not extend to business or commercial users."