Your site is behaving properly, why do you not think it is? The content container gets narrower, the sidebar collapses under the main content and the menu changes to a drop down menu.
If you're referring to the text in your header image, the reason why the text (like site title and description) don't resize or shift is because the "text" is actually part of the image, it's not really text. If you look at the demo page, the site title is actually text in h1 & h2 tags. Images that are a background property don't resize. If you resize the demo page, you'll see that the header image remains the same size.
If you go to your general settings page and fill in the site title and site description fields, you'll see that they will, in fact, respond properly (they just won't look as pretty as the text that's part of the header graphic).