yesterday I bought Gothic 1 and 2. I only installed Gothic 1 throught GOG-Galaxy. Today I was unable to run game, it only show on Task Manager but window is not shown etc.. Then I turn on internet and Gothic 1 start up immediately. I watched outgoings protocols and Gothic 1 start some action for online check.

How can I turn off this online check on sturt up?

Check the shortcut you use to launch the game: since you installed it using Galaxy, the shortcut is probably configured to launch Galaxy rather than the game itself.
In other words, browse to the game's folder and launch it directly using its own executable.