Okay, I'm going to say something, and it will sound rude. However, please accept it as a statement about the situation and not an effort to insult you. The apparent rudeness is a by-product of an earnest attempt to help.
As you can see from the photo's all the save button does for me is, essentially, exit the game without saving.
What I see is that you do not understand how the operating system manages folder information.
(There! That's it! No more rudeness!)
Everything else these folks have said to you is true, but you will be delighted to know that the game
has saved: it's just that the Windows operating system (
not Mac) doesn't change the "date modified" entry on a folder when the folder's contents change. Really! Test it for yourself by making some other folder, putting a file (like a .doc) into it, then modifying the file. Nothing happens. Are you perhaps accustomed to a Macintosh system where the folder "date modified" entry does change?
Here, just go back into Dwarf Fortress and load up region1-sum-251-win-win-252. You will see (and I guarantee it) that your game has advanced one day.
In the future, be sure to do as Quietust advised and just use "region1." It makes it easier to remember which of the unchanging-"date-modified"-info folders is the right one. You use the seasonal backups only if there has been a problem with your main save.
--Rexfelum