I've just installed New Vegas off-line version and puzzled to see it trying to contact 77.79.249.151.

It's not affecting the game playing as I was able to load a previous save from my Steam installation and play.

However, this seems a very un-Gog thing to do.

Why is it trying to contact GoG?

Even if not the exact complaint, I believe that you may be referring to the same issue that has plagued this game (and a number of other GOG games) for quite some time. Although, you do not seem to be affected by the launch-preventing problem mentioned within that separate thread.

With this game (among certain others), whether or not GOG Galaxy is installed, Galaxy.dll (within the Fallout: New Vegas installation directory) will attempt to contact galaxy-log.gog.com (which seems to be a method for interacting with an already-running GOG Galaxy client). This may be due to its support for uploading save data to the GOG 'cloud'.

Thanks, that's helpful. It's the same situation - apart from mine running without issue.

Try renaming the DLL to something else and run the game. If it works, great. If not, rename the DLL back to the original name.

Fallout: New Vegas requires Galaxy.dll, as GalaxyWrp.dll depends upon it. Deleting (or, renaming) Galaxy.dll will prevent the game from launching, as will the removal of the reference (via a hex editor) to Galaxy.dll within GalaxyWrp.dll.

The files of the GOG version of Fallout: New Vegas are sourced from a build meant for another platform. GalaxyWrp.dll basically simulates the API dll of that platform, and, for that reason, it, too, can not be deleted (nor renamed).

In my experience, the presence of both Galaxy.dll and GalaxyWrp.dll (in their non-empty file form) are necessary for running the game, and the only known options to neutralize the undesired behavior of Galaxy.dll are the simple circumvention techniques described within the link that I had previously posted.