Hey Mike. I've been receiving many crash reports from older versions of the game, and I've been looking around for ways to create auto-updater inside the game, but I don't think it's feasible to do it, because it would take a significant development time and would imitate itch.io app (would require authentication to itch.io, some diff for the game files, etc.).
I was thinking about putting a check inside the game that will notify you if you're playing on the latest version on the main menu screen. Unfortunately, it still requires a full, manual download from the itch.io website without the itch client.