Asking this to clarify is "Hex Kit" this program off itch.io : https://cone.itch.io/hex-kit or some other program? The screen shots seem to match but I'd want to know for sure before buying a program that it'll open your .map file. Originally I was excited because I thought it was a save file for https://azgaar.github.io/Fantasy-Map-Generator/ (which is GREAT and free but isn't strictly for making hex maps, it's more of a map creator that you can overlay hexes on) but you giving us a save file for any map editing software is an amazing plus and appreciated, it's just if I am going to spend money I want to make sure I am buying the one everyone here is praising so much.
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Yep, that is the program. You would also need to buy two tile sets: Fantasyland Tileset and Traveling Through Dangerous Scenery Tileset. You can also find the program and Tilesets over on DriveThruRPG (which is where I originally bought them): https://preview.drivethrurpg.com/en/browse?keyword=hex%20kit. Altogether, it costs 30 USD for the Hex Kit program and the two tilesets.
And thanks for sharing azgaar's Fantasy Map Generator, I had never see that before, looks cool!