I also seem to be having this problem. My phone is running the latest Android version available. For whatever reason when the download is completed, when I tap the icon it tells me the file cannot be read/ran.
Viewing post in Android error
itch.io didn't notify me of these replies and that's bad because that made me think there was no more issues with the android version, so I'm sorry for the late reply.
I have had a similar issue before from clicking right on the downloaded .apk from the downloads tab that pops up.
The way to fix it for me was to use the file manager app and go through it onto the downloads folder, and click on the .apk file that way.
I don't know why but for some phones just clicking on the download directly doesn't work. Could be since you may have downloaded from a browser, that the phone tries to open the .apk in-browser when you tap it.