I've never tried it, but I think you'd just set a WebView as the content view of a transparent borderless window, and tell the WebView not to draw a background. That way, the content of the WebView would define the window boundary.
You create a borderless window by passing NSBorderlessWindowMask to the -initWithContentRect:styleMask:backing:defer: method of NSWindow, and you can set its background to transparent by calling [window setBackgroundColor:[NSColor clearColor]].
You'd have to handle dragging of the window etc yourself. It will probably get a bit messy.
To be honest, it's not something I'd attempt as a first Cocoa project.