OK, I've checked this out. It looks like that's what Android does while it's preparing the package to be processed by the installer, so it should be a case of waiting it out? On my device (a oneplus 3, so quite high-end) that screen appears for 5 seconds or so, before moving on to the install prompt proper.
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Holy geez, this is a first for me. Usually applications (even sideloaded from SlideMe, FDroid, or whatever) pull up the permissions dialog very quickly. Waiting for a few minutes on that screen worked for me. That said, this is the first time I've tried to run a RenPy game on Android, so that might contribute to it.
Thanks!