Seeing this game stating a minimum requirement of Win7, I checked it on Steam and it says the same there too.

However, going through the patch notes (as they are visible on Steam via the game's Discussion forum) it does say in version v1.27672: "We've deployed a small update with a potential fix for the game not loading in Vista and XP."

In patch version 1.27825 (the latest at present time?) it then goes on to state: "our latest update should fix ongoing issues with older versions of Windows" and "Fixed crashes affecting some systems with Windows Vista or XP after recent updates".

From the above, it would seem that the game does in fact run on XP and Vista, and as these updates came from the developers themselves, I wonder why they never updated the requirement specs to include XP and Vista?

Should anyone be interested in reading the patch notes, here is the link:
http://steamcommunity.com/app/237930/discussions/0/540742485350246679/

Does the GOG installer come with the latest version, 1.27825? I would imagine it does, but confirmation would be great.

Yes, it does: http://www.gog.com/forum/transistor/patches_for_gog_version/post2

So why don't they list XP and Vista as supported OSes, being as they patched the game for issues on those OSes?