I believe your (apparently simple) question implies a couple more questions, so I'll try to split that up and address each one separately:
1. Why does my "panel" look different than Hangouts ?
Hangouts opens as a panel (so it is styled as such).
Your "panel" opens as a popup (so it is styled as such).
2. Why does my "panel" open as a popup ?
In order for an extension to be able to open panel-windows, the user must have this (experimental) feature enabled (and of course the underlying OS must support it). If panels are not enabled, all windows of type 'panel' or 'detached_panel' open as type 'popup' (documentation).
3. How can a user enable panels ?
Navigate to chrome://flags/#enable-panels
and click Enable
.
4. How is it possible for Hangouts to open panel-windows when the flag is disabled ?
Short answer: It is white-listed in the source code.
Longer answer: Take a look at this answer.
5. Can I style the title-bar of a popup ?
Not really. The title-bar displays (among other things) the title of the page, so you can customize that part :)
6. Do I have an alternative ?
If you absolutely need to be able to style your window, you could use a Packaged App. Apps can open frameless windows, so you can create (and style) a title-bar using HTML/CSS.