This question has been asked by me and a number of others. The developers of the app have stated that third party downloaded games will not be supported in the app.
Viewing post in Manually installing games in itch app
Which is funny seeing as itch.io keeps shrinking upload sizes, which cause Dev's to have to upload to 3rd party sites in the first place.
That being said, there's a few games/VN's that I have had installed through the app that are over 2-6GB. One installed right now @ 9GB, so it's confusing why and when the upload sizes got severely cut so that even most 1GB games have to go through 3rd party sites as well.
Talk about itch.io cutting their own balls off when it comes to favorable app statistics.
If anything, at the very least, make it so ppl can add these games TO the app list if it's something they had to d/l from 3rd party, BUT only what gets recognized as already originating from the app. But of course that's probably too close to how other companies solve their compatibility problems (cough, cough, St3@m), that they don't want to do it.