Here is a thought that might get me laughed at... but, nothing would really stop you from making something in Construct, taking a screenshot at runtime, cropping it in another program like GIMP or Photoshop (similar to what you did in your initial post), and then uploading the picture file. From there you could add links on top of the pages you uploaded while inside the webpage uploader console (most hosts have them). In reality, all a webpage is is a visual with clickable links to take you from page to page.
Having said all of that, if creating websites from scratch with a strong code base is the goal, then there are programs specifically designed for that which I think would be much better suited for building a full-fledged website.
I don't think that's what he was asking, he wanted to know how to display a webpage in a game or app, which maybe the http object does, but I've never used it, nor do I know how...i think it's mainly for formatted text. could be wrong though. also, this belongs in help/tech support