Note: This should work the same for many future versions of Factorio.

For anyone who has noticed the Steam has 0.15.1 release and found that it isn't available through Gog yet, you can still download it (after jumping through a few hoops).

If you own the Gog version of the game and have a Factorio account then you can download 0.15.1 from the https://www.factorio.com/download/experimental website.

Your factorio.com account will require you to enter the Serial Key at some point.
To get the Serial Key log into Gog.com, go to your games, select Factorio, then click more and select "Serial Key".

NOTES:
The https://www.factorio.com/download has the stable releases.

I have no explanation of why Steam lists 0.15.1 as the latest release while the Factorio.com website lists it as an experimental release. I can speculate that maybe Steam users are being used as proverbial guinea pigs, but I really don't know.

Obtaining the Serial Key via GOG Galaxy is not possible because of course it isn't.

Both on Steam and on the game's website v0.15.2 is already available. It includes quite a few bugfixes:
https://forums.factorio.com/viewtopic.php?f=3&t=44920 If you are referring to the news on the store page: The developers have always posted the latest release info there. However the Steam client will only download experimental releases, if you enable Beta participation in the options.

I've just created a new Factorio account in the hope of getting the new update, but when I go to the experimental download page the download links listed are for the headless version to run on Linux. Also the normal downloads page is only the free version because my accounts is only the free one because it thinks I haven't bought the game yet!

How/where did you get the option to download the latest Windows version (0.15.1 I think) and enter the GOG serial key?

Have you upgraded your factorio account?

Put the GOG CD key in the upgrade account box in account settings.

Yeah, I just worked it out after posting this, got the update, thanks. :)

No problem =)

I think my confusion stems from when I watched https://www.youtube.com/watch?v=wJnLcIBwqHA then went looking for more info and found the Steam headline "Factorio 0.15.1 released" and assumed that the game was released in a fit-for-general-consumer-use way. The Factorio people seem to use use the terms "Experimental Release", "Stable Release", and sometimes just "Release" which is problematic when the word "Release" is not qualified.

[rant]
I come from back in the day when a "Release" was more or less a final product (occationally getting updates or rarely needing a patch to run correctly) and terms like an update and patch were not interchangable. I know that the meaning of words change as people use them but at this point calling something a "Release" means exactly what the person who wrote it means and nothing more. To put it another way it was not clearly communicated if 0.15.0 was a Beta or a Stable build.

So over today and yesterday they "Released" 0.15.0, 0.15.1, 0.15.2. This is quite responsive as development goes, but I wish they would just call these Betas instead of a "Release". The term Beta exists for a reason.
[/rant]

At least the Factorio people are not making the Stable Release avilable on Steam then to Gog when they feel like it which was my initial fear when I realized that 0.15.0 was "Released", but not available via Gog.

Valer1us, thank you for the reply. It did help me figure things out quite a bit.

The only indicator for it being a Beta Release was the last sentence in the news: "You can get experimental releases by selecting the 'experimental' beta branch under Factorio's properties in Steam."

Let me throw in another term: "Early Access". Some modern fancy wording for: a Beta that you have to pay for. So, v0.15.x... -- is it an "Unstable Early Access Experimental Beta Release"? :)

But jokes aside: I am glad to read that there is actually a way for all the GOG users to get the latest version. 0.15 is a huge update, and so far I have enjoyed the new science setup quite a lot.

Let me try this again.
It was not clearly communicated if 0.15.0 was a Beta or a Stable build in the title "Factorio 0.15.1 released".

The title needed to make the distinction because this is when it has the reader's full attention and before the reader's mind starts filtering out other information. If they used a title such as "Factorio 0.15.1 Beta released" then they would be working with human nature, but buy spelling it out at the tail end of the article the mind will often discard it after reading it without processing it.

If you read the article's comments you will see multiple posts like the following ones.

"how can i get the updates? i.e. 1.15"

"i cant get 1.15 update why ?"

"why I can`t update?
my factorio v.14.23"

Also Early Access means in development and can have beta and stable builds.

On the website Valve basically says "This Early Access game is not complete and may or may not change further. If you are not excited to play this game in its current state, then you should wait to see if the game progresses further in development."

I know what you have posted is meant as a joke, but these jokes do seem to perfectly mirror the erroneous assumptions about what is being communicated. The three quotes above I copied from the first three pages of http://steamcommunity.com/games/427520/announcements/detail/1290688221280058724 so with that small sample it looks like about 1 in 10 people are having the same problem. I'm not going through all the pages to get an actual (or even credible) esitmate, but it does seem to be a lot of people who where miscommunicated to.

The upside is that because miscommunication (in general) exists there are a lot of Call Center jobs that wouldn't exist otherwise.