There should be an indicator on the front screen that the game has an update available.
The instruction for updating are here :
https://killerbeesoftware.itch.io/empire-deluxe-combined-edition/devlog/16579/it...
If you are a Kickstarter backer, you should use the original link you were sent to access the files. Otherwise, they should be accessible through your itch account.
--Mark