If you have a 1.31.1 installation, it is possible to run the game from:
Game: <installPath>\Warcraft III\x86_64\Warcraft III.exe
Editor: <installPath>\Warcraft III\x86_64\World Editor.exe
First time you run, it will open a launcher-like thing where you will have to enter your cdkey (yes, it requires a cd-key and NOT a Reforged licence).
It is not possible to play on battle.net, you will have to use a LAN-emulator (for example ZeroTier) to play with friends online (on "LAN").