The patch is just an rpa file. Extract it. Locate where itch installed the game onto your computer, and move the rpa file into the 'game' directory. The 'game' directory is a directory titled 'game' inside the actual game's install. You'll know you have the correct spot if you see a file titled 'archive.rpa' inside it.
If you don't know where itch is installing things onto your device, I think that it uses '/home/[user]/.config/itch' as the main install location. Check there and see if you can find anything related to Dawn Chorus.