You want to show your YouTube or Vimeo video on a page in your branding. Then add your video to a web page within Spotler. You do this by using the editor options on the left.
Like a content block, you can drag a video block onto your canvas. Then double click on the block and enter the URL of the video. Click on Ok and voilà your video will be shown on a page that fits your branding. When you preview the web page, you will also see the play-functions associated with the video.