I get the same message that my internet is NOT connected. I tested it with an Linux PC, by tracing the connection, everything's fine, inet is always up on my side.
Sometimes the error messages are misleading. It can be a mixture of timeouts caused by too much traffic at the AppStore, a download file that simply cannot be installed, like Jay O.'s experiments suggest, it can be aproblem, that the App Store cannot be contacted for other reasons - a firewall or antivirus software interfering, a problem with the AppleID, a permissions error in the user library, etc.
It would help to know, if someone actually could install the complete update. This way we would know, that we have to look for the problem on our macs. For me, the drum kit "Manchester" is still missing.