Just checked, printed page looks close to that online print view display.
Note that your website has special styles for print view in templates/beez_20/css/print.css that affect look, that's why you have no one-to-one correspondence.

Let's make it clear that the online print view is somehow different from the printed page layout.

The printed page layout of my website was OK bevor I updated to Mobile Joomla! 1.2.3. After this update the printed page layout was damaged. I cannot use it anymore.

If you don't provide a solution for this bug, I will have to re-establish my website without Mobile Joomla.

Design of your printed page is (mainly) rules by templates/beez_20/css/print.css file. It's clear that your file is not initial joomla's file (difference in font size and weight), but in general design of printed page is close to default beez_20 one. The only exception is Most Read Content module (but default beez_20 doesn't support it as well, it supports menu module only) and Catchwords module (it's 3rdparty module).

MobileJoomla cannot affect desktop template at all, you can check it in sources.