Zoolz stores the backup settings and the machine information in your (%appdata%\Genie9\Zoolz). When you move to a new machine, these information will not be available there.
So now, when you download and install Zoolz on your machine, and sign in to your account, if you have already reached the maximum number of computers*, you will be asked to delete or archive the older machines in order to be able to add the new machine.
The good news is that Zoolz has a De-Duplication feature that will prevent uploading the same previously backed up files again. For more information, please refer to this article.
* Zoolz Home users can back up one (1) machine only, but Zoolz Business users can back-up up to three (3) machines per user.