+ AA6YQ comments below
Thanks Dave, but my Windows 10 is running fine reliably and without any other (noticeable) problems.
I have found simple way to get the effect. I now have DXView pinned to the Task Bar. Click on it to open it. it can be seen in Task Manager as an App. When it's opened fully, close it from the Task Bar by clicking on the X in the corner of the popup. It the moves from the Apps in Task Manager to Background Processes.
+ I have replicated this behavior on my Windows 10 system. Letting the mouse cursor hover over DXView's icon in the Window's Task Bar and then clicking the X button in the upper-right corner of the resulting popup causes DXView's windows to disappear, but DXView remains running in the background. In contrast, right-clicking DXView's icon in the Windows Task Bar, and selecting "Close all windows" correctly terminates DXView, as does clicking the X button in the upper-right corner of DXView's Main window or directing the Launcher to terminate DXView. This is clearly a defect in Windows; if you want to pursue it further, please engage with Microsoft Support - and post your findings here.