Hi there!
I'm not a professional in IT, but I can certainly try! Is this a problem you've had only with this game or any APKs you've downloaded through itch.io?
If it's the latter, the problem may be with your permissions regarding third party apps. Essentially, a security feature of your phone makes it, by default, prevent any apps from a source that Samsung does not recognize, including Itch.io. To allow your install to proceed, you need to go into your settings => Apps. Then from that screen, at the top right, select the menu and choose "Special Access". Then from the list, select Install Unknown Apps. You can then select the browser from where you downloaded the APK, download the app again, and it should install :)
If that doesn't work or if you've never had an issue with APKs from itch.io before, let me know! I'm not sure how I could fix it, because i just tested out the download on my phone and it works fine, but maybe I can find something else.
Thanks for stopping by!
Drac