Hello!
The free version is an older build use as a demo. If you paid, you downloaded the 0.11 which is just the update. And I'm still working on the game to add more content.
You don't need to install anything, just unzip it somewhere on your computer and ... that's it. You can keep the older versions of delete them. They all use the same saves so you won't lose anything.
About steam, yes I just opened a page for the game: https://store.steampowered.com/app/1698670/Daggan/
Kisses