Hi there,
When using the non-DRM version there's no automatic updates. You'll need to go back to the Humble site to download the updated version. Then follow the same instructions you did when originally installing the game to copy the new version on top.
If you didn't create an account on the Humble site you can use this
Order Resender to gain access to your download page again.
All the game's preferences and save files are stored separately, so you should not need to worry about losing progress.