You can check the box in site manager that tells DW to "Automatically upload files to server on save", but this is not recommended. If you are editing a page and hit save, it will upload it regardless of it's state and you can lose work as a result. Use with caution.
I agree with bregent - it's a very dangerous option to enable. You're much better off saving the file locally and then just using PUT to upload to the server.
That site is built with WordPress. Owing to the dynamic nature of WP, once your site is deployed online you really must use the online CMS (WP Dashboard) to edit pages. If you don't, you could break the site.
See using WordPress