No. You do not need to buy the game again.
The only inconvenience you now have is to re-download the game with every new version :D
Thank you for your support and trust.
To download the latest versions upon release, you will have to go to the link which was send to you by itch upon purchase, or you can find it in your library.
I also recommend to download the itch app for windows / Mac as it updates the game automatically for you, just like Steam.