You got an email with a link to your download page. If the game is on your account, go to your library and there to the purchases. Or visit the game while being logged in, it should read above the game, that you purchased it. If you click on Download there, you go to the download page where you can redownload.
But if your file does not work, it probably was affected by the current download issues across itch, resulting in corrupted downloads without error message.