I downloaded a Mac version of the game and there seems to be network game missing. The menu item which has the network game option in Windows is completely empty. Is it true that there is no network game in Mac or what could be the problem?

www.gog.com/game/airline_tycoon_deluxe says (just below system requirements):

"Multiplayer notice: The multiplayer mode featured in Airline Tycoon Deluxe is supported on Windows ONLY. "

So yes, network games are apparently not supported at all on Mac or Linux.

:(