You can absolutely use time machine backups with a different Mac, the process is slightly different but still works.
Migrating a Time Machine backup to a new Mac
When you buy a new Mac, you can transfer all of your applications, files, settings, and other information from a Time Machine backup you've already made.
You will be asked if you want to transfer files when you start up your new Mac for the first time. Or, you can use the Migration Assistant (located in Applications/Utilities).
After Migration Assistant completes the transfer and you select your existing Time Machine backup drive, you will be prompted with "Inherit Backup History". Once selected you will be able to continue to use your existing Time Machine backup on your new Mac.
Migrating a Time Machine backup to a new Mac
When you buy a new Mac, you can transfer all of your applications, files, settings, and other information from a Time Machine backup you've already made.
You will be asked if you want to transfer files when you start up your new Mac for the first time. Or, you can use the Migration Assistant (located in Applications/Utilities).
After Migration Assistant completes the transfer and you select your existing Time Machine backup drive, you will be prompted with "Inherit Backup History". Once selected you will be able to continue to use your existing Time Machine backup on your new Mac.
http://support.apple.com/kb/ht1427