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I believe that you already know this but, Steam requires to internet to play online games.
Ark's server will firstly connect through Steam's https://partner.steamgames.com/doc/features/multiplayer/game_servers to be shown on the server browser(either Steam's server browser and Ark's server browser), so that any steam user can find your (or, others) server from anywhere.
Since your server can't connect to Steam master server, the game cannot receive any info from it, so it refuses to connect. I don't know what would happen if you gone completely offline, but my bet is that you can't even select connect to multi player server.
Or maybe perhaps you can connect through console. When you start your Ark, hit Tab to open console, and then type open 127.0.0.1:7777 (or whatever port you've forwarded), and hit Enter. I don't know if it works, but maybe give it a shot.