Some games have "(gog-x)" version number, for instance "(gog-2)" or "(gog-5)". According to GOG support this is GOG's "internal" versioning scheme. Does this mean that the developer hasn't provided a version number? Does the number change sequentially from "(gog-1)" ("(gog-1)" > "(gog-2)" > "(gog-3)"...) when the game is updated?

Yep.

But that was the old system. Since a couple of months ago, this versioning system has been phased out and for new updates GOG is using each game's actual version (i.e. the one provided by each dev).

Not only the game, it was rather the version of GOG's installer. Sometimes only the installer got an update, while the game stayed the same. Versioning has always been a weak spot of GOG. It has never been consistent. However, like muntdefems said, they dropped this system for new updates and provide the actual version of the game (most of the time).

Are they not also using their own release numbers? I was under the impression that they used the actual game version and added a number for the GOG release (which is useful if the packaging needs to change for whatever reason, but the game itself hasn't - for example GOG figures out a better default for compatibility settings, or they update the included DOSBox).

I'm most likely not entirely up to date with these details.

You're right. They do include GOG's own release number in the file names. In the library, new (or updated) game installers usually are listed with the game's own version, while new patches usually specify which GOG release number should be applied to, and to which GOG release number will it bring the current installation. Rather confusing, if you ask me.

GOG used an old filename scheme like this:
setup_kings_quest8_2.1.0.26.exe
setup_ishar2_2.1.0.26.exe
setup_chinese_chess_2.1.0.26.exe
setup_battle_chess_2.1.0.26.exe
setup_red_baron_2.1.0.26.exe
setup_battle_chess4k_2.1.0.26.exe

And GOG used to show only the last number in the download page, so people could see if they need to download the updated installer.
For example, if you found GOG provide a gog-27, while you only have 2.1.0.26, then you should download the new installer (something like 2.2.0.27, another stupid versioning system, I'd say).

After GOG drop the old filename scheme, some installers provide the gog-* system, to match the old behavior.

However, many new installers provided by GOG, never follow the backward compatible scheme.

GOG's recent installers have very bad and ugly filename scheme, typos, wrong versioning, and often forget to bump version/build number.
(That is, GOG provide different files, but have exactly the same filename.)

GOG's installer management have (at least) a very big problem.