In general it's quite clunky to keep games updated if you ask me.
The itch.io app is somewhat useful but the reason I stopped using it it because it doesn't work with games that aren't hosted on itch.io.
You can't even install the game yourself and then point the app to include the game as far as I can tell, meaning that you can keep some games up to date using the itch.io app and other you still have to download manually.
If the itch.io app isn't for you then my suggestion is to follow all games (and creators), regularly check your feed for any updates to the games, and then download and install the update manually.