I used to  download some games from itch. io  and now i downloaded this desktop app

How can I move the previous game data into here?

I'm sorry if this question has been asked

you mean the download files or the game data? the game data would be the save game, that does usually not change if you change installation data.

if you mean how to make the game be updated by that itch app, but not download it again, since you already downloaded it, no clue. but you can add installation directories.

you probably are following developers of your games, so, my first guess would be to just add the game to the app after an update, so you reduce unnecessary downloads.