So it sounds like you only copied some dylibs and the Frameworks directory? It's not completely clear to me if you've done this, but you basically need to copy the entire game directory to the other computer first. In this case I mean
~/Library/Application Support/Steam/SteamApps/common/Counter-Strike Source.
On the other computer, you can then name this directory whatever you want. After that is when you would add the files from the srcds_osx package as well as copy the other dylibs and Frameworks from /A/S.app/C/M/ and /A/S.app/C/M/o.
Also note that you'd probably need to copy the game files again whenever there is an update to CS:S. You could look at the last modified dates to figure out which ones were actually changed or use
rsync to copy them. I realize that's not ideal, but that's what you'd have to do since there is no steamcmd available for OS X.
In my opinion, it would be easiest to download and update the games directly using the regular Steam client. You don't need to actually run Steam or be logged into an account to run the server. That would only be necessary for updates.