There are two concepts regarding closing features, which don't feel natural on the Mac. Current behaviour: 1. When the last tab is closed, the window stays open e.g. a new tab is created. 2. When the last window is closed the app quits. Are there specific reasons for that behaviour? How I think it should be: 1. The window closes with the last tab. 2. The application stays open without a window.
The way it behaves now feels more natural and consistent to me. When I close an application window, I expect that application to be closed; when I close all my tabs in a text editor, I expect to then be able to start working on a new file from a new tab without needing to restart the application. In the same way, I do not want to have to restart Vivaldi after closing all of my tabs, and I do not want it to continue running after I have close the window.
That said, most browsers behave the way you describe by default, and I can see why not closing the browser with the last tab might seem inconsistent and odd to other users. It would be ideal to make this a configurable setting, as that is kind of what Vivaldi is all about.
In the mean time, there are Chrome extensions that will close the browser to the tray and keep it open in the background when you close the window. This may not be exactly the functionality that you're looking for, and they may or may not work with Vivaldi - but they do exist.
The behaviou you're describing might be correct for Windows application and mostly Linux GUI applications as well. But it's not the behaviour you expect on a Mac. Cobbler, stick to you thy last and let the Mac Users decide what feels natural on a Mac.