Restore Time Machine backup onto different Mac
There are a couple different approaches you can take.

Approach 1 - Erase the newer iMac, reinstall 10.6.8 and use migration assistant to migrate your Time Machine data

With the newer iMac:


Insert your Snow Leopard DVD (not the gray disc, a retail copy) and boot to it either by holding C while powering on or holding option while powering on and then selecting the 10.6 DVD.
Select "Disk Utility" from the Utilities menu in the Snow Leopard installer
Select the iMac's hard drive from the list on the left in Disk Utility, click on the "Erase" tab, type in a name for the hard drive (Macintosh HD?) and click erase.
Once the hard drive is erased you can close Disk Utility and proceed with the installation of 10.6, following the on screen prompts.
Once the installation is finished your newer iMac will boot to the normal welcome to OS X screen.
I believe the third or fourth step in setting up the newly installed 10.6 will ask you if you want to transfer information from an existing Mac.  Make sure your external Time Machine disk is connected and choose the "From a Time Machine Backup" option and follow the onscreen prompts.
Once the migration is finished you should be able to login with your normal user account and your data should appear to be just as it was the last time your old Mac backed up.


Approach 2 - Clone your older iMac to the newer iMac

This requires that you have a firewire cable

With your older iMac:


Download Carbon Copy Cloner on your older iMac
Power on your newer iMac while holding T, you should eventually see the Firewire symbol (sort of looks like a Y) floating around it's screen
Connect the two Macs together via a firewire cable, your newer iMac should appear as an external disk on your older iMac's desktop
Open Disk Utility (/Applications/Utilities) on your older iMac
Select the newer iMac's hard drive (should be an orange icon) from the list on the left in Disk Utility, click on the "Erase" tab, type in a name for the hard drive (Macintosh HD?) and click erase.
Once the newer iMac's hard drive is erased you can open Carbon Copy Cloner
Follow the on screen prompts in Carbon Copy Cloner to select your newer iMac's hard drive as the destination and then clone your older iMac's hard drive over to it.
Once Carbon Copy Cloner is finished you should be able to boot your newer iMac and browse through to see all of your older iMac's data now in place.


Hopefully one of those options works and you're able to get that data migrated with little to no pain.