In the Print dialog, under View and Output Scale, when I choose the Window option the result doesn’t come close to matching the preview in the modeling window.
From the video it seems that the window selected does match the printed preview.
Use the Viewport option to set it to the whole viewport window for output.
I tested it here to see if I could get it to mess up.
Oh, somehow my selection window is taller than my viewport. How did I do that? I thought it was showing my page height as being my whole rhino viewport.
It is on Portrait papersize. This can vary based on the printer itself.
So to me it looks as expected. But perhaps you want landscape paper?