Yes, convey separation, but after a certain number of pixels white space is not as effective anymore. Notice how in the example of the table he argues that for wider tables using white space is not effective, and that delineation using colors should be applied.

The brain has to look at a layout and make sense out of it. In real life we're aided by contrast to make sense where one object starts and where the other begins -- without contrast you end up with camouflage. When using white space our brains figure out the delineation based on positioning. If blocks of text are perfectly aligned we fill out the delineation automatically; so lines are not necessary. This process breaks down over large areas since our field of vision is small and we would have to scan the whole area before we would make sense of it.

In the new Gmail layout, the menu items are aligned to the left, and so is the content. There are no "lines" between the menu and content the brain can fill out. Of course we can tell where one stops and the other starts, but it takes longer, it wastes more brain cycles than necessary.

Based on the screenshot we do no see the same version. In your version you have a separation between the menu area and the body of the email, the buttons have text and not icons, so we're not arguing over the same layout. Also, I do not see a classic theme being available.

EDIT: I don't see a classic theme that would look like your screenshot.