Good news, you too can run Minecraft Alpha 1.2.0 single player offline without signing in. That's not what made this impressive :).

Try the "Windows Legacy" launcher, or a 3rd party launcher like PrismLauncher. The legacy launcher is made for Windows 7 and is directly equivalent to the macOS/Linux launcher, so it doesn't have a hard dependency on the Microsoft Store. It will probably be a while before they stop maintaining it because it's such a trivial port.