The current beta does not rely on Growl at all. I can see two possible reasons of your trouble (or combination of both):
(1) You are not trying to install from the latest beta, but an older one.
Please double check you are using the image you can download from this URL:
http://public.avast.com/dev/mac-beta1/avast-28264.dmg(2) An older version of avast! was installed and you haven't uninstall it before installing the current beta. If this is the case then take a look into /Applications and check if there is avast!.app present. If yes, try to delete it. If it fails (I guess so, it shall tell you that something in the folder is in use), then follow these steps:
* Delete file /Library/LaunchAgents/com.avast.MacAvast.LaunchAgent.plist
* Reboot.
* Try to delete /Applications/avast!.app again. Now it should succeed.
(Please note that this inconvenience is fixed in the current beta so upgrades to future versions from current one should not fall into this trap anymore.)
Regards,
Mity