Hmm, my Playnite picks up my itch.io games no problem, including free ones, I think, so long as they are listed in my itch library. However, I do have the itch.io app installed on my PC, and it's possible that Playnite is drawing its data directly from the app, and not from the account itself (since all it really does for pretty much any game from any platform is open up the platform - so, if I click on a steam game in Playnite it will open steam, if I click on an Epic game, it will open Epic, etc.?) It seems to piggyback off of the existing launchers, is what I mean. Do you have the standalone itch launcher installed?
That aside, you can also add games manually by creating an entry and pointing it at an executable. You can also even get emulators and emulated games listed (with all proper legalities considered, of course).