By following these steps : https://itch.io/t/1128078/how-to-download-the-updates
I think you have to get back to the Email you got after buying the game without an account, for people without an account they ask for a email adress to send the product to and it directly link to your email adress so open the email they sent you when you bought the game and click the link, it should lead you to the download page with every files Grizzly Gamer Studio put there, including the updated one
If you don't have the email anymore or lost the URL, go to the Support Page and ask them to email it to you again
Also, maybe it's worth asking them to link the game to your newly created itch.io account so you won't have any problem later
Please, note that I am not in any way related to itch.io staff or customer service, so I might got some of those things wrong but that's all I remember from when I bought the game, even though if the email thing still doesn't work, you should reach out to them using the Support Page and they'll find a way