Check all of his router settings, not just the firewall.
Starcraft II uses TCP port 1119 to play and UDP port 1119 for in game Voice chat.
The StarCraft II launcher uses TCP port 1119, 1120 to obtain patch information, and 80 to get to the web site for patch notes.
The StarCraft II Downloader uses TCP ports 3724 and 6881 through 6999 for Peer to Peer (The Downloader will use 3724 first and if it's not available, move to 6881 and on up to 6999.)
Patching the game requires TCP port 80
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