Just bought a game with GOG and first downloaded the offline installer setup file (5835), so I installed the game.
Then I started GOG desktop and noticed it had an update to a newer version (6004).... ????

Yes, sometimes the offline installers are an older version than the Galaxy version. Short of asking the developer to update the offline installers, there isn't much you can do unfortunately.

This happens quite rarely. By now it should be automated. In some cases the offline installer was not updated when all they did was adding cloud support for save games - which would require Galaxy anyway. Then Galaxy would download the update.

Which game is it btw?

According to the table, Tiny Thor.

And yes, there are a bunch of games with outdated offline installers, and not just briefly.

There's also a few games that don't have updated patch notes so you have no idea of what the latest patch does.

Now that each new update may easily come with changes that break existing compatibility with older Windows versions, it would about time for GOG to make it impossible to submit a patch without filling a change-log field, of course it wouldn't prevent developers inputting just the bare minimum of characters to pass or just a copy of the previous change-log, but at least then it would be undeniable that they chose to not provide the latest change-log to us rather than forgetting in a hurry to fill some optional fields.

Lets just say that it is not fun to have almost two dozen DLCs for Dying Light and then see that the game has a new update without a change-log, as installing that update will cause the Galaxy client to edit the registry entries for every installed DLC and that means a lot of extra UAC prompts that a single player gamer might wish to skip whenever the update only fixes multiplayer issues or adds textures and models for a new DLC that they at least currently are not interested to unlock.

I'm a little lost. Looking at Deus Ex offline installer is 1.112fm(Revision 1.6.3.0), and Galaxy is 1.112fm(Revision 1.6.1.0). Is the Galaxy version outdated??

There are a few others like that on the list. It actually tracks differences, not just when the offline one is older. And a blue said at one point that sometimes there may be version numbering differences.
I even wonder about the case of Tiny Thor, since GOGDB says that 6004 was added before 5835, wonder if it's some case of a regression being needed for the game to work without Galaxy installed, so when the OP started Galaxy it obviously detected that it was in fact installed and grabbed the Galaxy-tied version.

Both Versions have different patch numbering, but could be the same update for some games? If that is what I understanding. I wish we got better patch notes for our GOG games.

Most of the time we don't get patch notes at all. Only very few devs always add patchnotes here.
The internal versions are very misleading anyway, you are right about that, so are internal build numbers (maybe even more).

The only indicator, if the Galaxy-version of a game is indeed "newer" than the offline version, is the GOG/Galaxy build number. Its a shame that gogdb doesn't show more details. The steamdb also shows what files have been changed from one build to the other. Of course that would compare two Galaxy downloads, but one of them would be the same as contained in the offline installers.

Tiny Thor

Looks like Tiny trooper got updated to lasted version as well.

You'd be surprised at how badly the system is managed sometimes; especially in terms of versioning schemas.