Turns out, the issue was not with google chrome, but actually with my Windows 10 setup. In
Settings -> System -> Multitasking
one has to set "Snap windows" to "On". This makes all windows draggable from a maximized state.
You can hit the Print button when viewing an individual email (icon that looks like a printer, in the upper right).
For me (Chrome browser), this brings up a simplified view of the email in a new tab, and a print dialog. Hitting Cancel on the print dialog leaves the tabbed view of the email, and this tab persists even when the main GMail tab is closed.