Hello mikiluki77.
The GOG version of Terraria is "not like steam" because it is
the GOG version of Terraria. But don't worry. What you and your friend need to do is to either:
A) Set up a Terraria Server. The server software for this is available for free in the official Terraria Forums. Here's the link to the current version:
1.3.5.3 Dedicated Server B) Alternatively, one of you can host a multiplayer world for both of you. However, if the player hosting it gets disconnected, the other one will get disconnected as well.
To do this, just launch Terraria. The Player hosting chooses
Multiplayer ->
Host & Play -> selects a player, creates a world* and sets a password.
The Player hosting chooses
Multiplayer ->
Join -> selects a player -> enter the hosts IP address, Port (Terraria's default is 7777) and password.
Depending on your connection, Solution B might lag uncomfortably. (I'm not familiar with Czechia's internet providers.)
Best of Luck and have fun with Terraria. ;)
* I strongly recommend a small world. "Small" is still pretty big for a group of 2 or 3.