No, Office 2008 works with Tiger, I'm not sure why the installer's opening up iTunes. Why can't you install it via disk?
P.S. Next time you make a thread give it a name that relates to the subject such as "Office '08 won't install on OS 10.4"
Edit: Here are the system requirements for 2008. Unless your computers 10 years old, it should hopefully fit these requirements.
• A Mac computer with an Intel, PowerPC G5, or PowerPC G4 (500 MHz or faster) processor
• Mac OS X version 10.4.9 or later
• 512 MB of RAM or more
• 1 GB of available hard disk space
• HFS+ hard disk format (also known as Mac OS Extended or HFS Plus) To determine the format of your hard-disk, click the Apple menu > About this Mac > More Info.
• DVD drive or connection to a local area network (if installing over a network)
• 1024 x 768 or higher resolution-monitor
To find this information go to the Apple menu in the top left of your screen and click "About This Mac". That should tell you your processor, OS version, and Memory (RAM).