I have the almost identical problem on MacOS (10.14) using the latest Vivaldi 4.
That is, on a desktop with no Vivaldi window in it, if I switch (Cmd-Tab) to Vivaldi and press Cmd-N, the File menu highlights from the action but no new window opens. However, if I use the File menu directly, a new window does open in the current desktop.
While you can navigate the menu using keyboard shortcuts in MacOS (by pressing Ctrl-F2, given that "full keyboard access" is activated, in turn toggled by Ctrl-F1, then use the arrow keys to go to the menu item and press return/enter), this is less known and less efficient. So I agree with the original poster that Vivaldi ought to do what most other Mac apps do, that is to open a new window in the current desktop when Cmd-N is pressed.