@SGaist yes, you were right! Qmake is saving absolute path internally, I think. So I moved all necessary files to required directory and everything is working, thank you!
I'll post a screenshot with minimum necessary files and directories that needed to successful qmake's work without Qt.
It requires an empty include directory! If you delete it QtCreator will not show your non-Qt Kit in the startup list of Kits for a new project!