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No, you won't have to purchase it again.

This is from the itch.io support:

After the purchase

The download page is the first thing the buyer sees after buying a game. Here is what it looks like:

itch.io's purchase dialog

At the top of the page is a detailed description of the transaction and any important information regarding how the download page works.

It reads:

This page has a unique URL for your purchase. You can always re-download the latest files from this page. You should have also received an email with a link to this page. If you ever lose the URL for this page you can request it to be emailed to you from the support page.


Yeah, after I replied to you I found that page!