You can match the desktop and the mobile views to both look exactly the same. However, you will end up with the mobile view being much smaller and narrow heightwise.
Think about it logically, desktop is horizontal view whilst the mobile is a vertical view, hence why you have the separate editors for each view.
Imagine your rectangular design which fits perfectly on your desktop view with the long edge horizontally…
Then place that same display onto your mobile view without rotating the display and you will have to scale down considerably the width of the desktop version, which would make everything on your mobile view very small.
Plus, you would also end up with a very large empty space underneath the bottom of that view.
Or, if you fill it with the website background for example, you will have a very large empty space on your mobile view.
Remember:
Desktop - Horizontal viewing;
Mobile - Vertical viewing.
Always best to have different but similar layouts for each.
Of course, you can insist that your website is displayed horizontally on your phone too by using code which would help you to match your desktop version.
However, this would mean everybody who uses your website on a mobile device would have to swap their mobile device from vertical to horizontal viewing and back again when they go to another website.
Which, if you think about it, would be very annoying after a while if users are visiting different sites at the same time.
Plus, for those users who have their mobile device locked so that it only displays the vertical view only and doesn’t rotate to horizontal viewing, well think about how your site would be affected when they went to view it and would have to scroll left/right and up/down to view your site.
Mobiles games are better horizontal viewing, however think about all your other apps and websites you visit and think about what way they are displayed on a mobile device.