Finally i fixed my code, and eliminated the "anachronistic old-style base class initializer" problem.

Now, i am back to the proper engine closing when the application stopped by clicking on its close button.

Finally i fixed my code.
Now i have a working application with its own window with widgets.
a. one groupbox that holds the engine window.
b. one button that starts the engine.
c. one button that stops the engine.
At last but not least, when the window X button senses a click,
the application closes the engine and the application itself.
No more task remains in the tasklist.
Thanks all the helps to everybody.

If anybody is interested in how to use Qt combined with Gamestudio, i can describe here my solution.