Well, This problem occurs in a very specific way etiher. I tried to figure out this issue for whole week, or more..
In my case, ( Joomla 3.7.2, Widgetkit 2.9.8 ) there was no conflicts, no any other possible reason, everything was OK but It wasn't working. There was no error in console.
I tried all browsers, (No extension, newly installed browsers.)
Finally I figured out something.
When I changed the mobile view in chrome debugger, in any phone layout, I could move the items by dragging. Then I tried a real phone, and still it was working perfectly again.
Then I realized.
My screen was a touch screen!!!
If you are using a touch screen on your PC, you can't simply use Drag & drop feature with your mouse. You should use it by touching and as you know it's not a common way, Well I have a touch screen but I never use it for this kind of purpose.
I had disabled touch screen on Windows Setting - Device Manager as it's stated here: http://www.thewindowsclub.com/disable-touch-screen-windows-10
Even if my touch screen is disabled, Chrome and all other browsers works as if it's active.
There is a flag setting in chrome: ( you can reach it by going to chrome://flags/ )
Touch initiated drag and drop Windows, Chrome OS
Touch drag and drop can be initiated through long press on a draggable element. #enable-touch-drag-drop
And this setting's default configuration works as touch, and simply you can't drag and drop your mouse.
So, the real soluion should be this: Drag & Drop feature should work by mouse even if it is a touch screen.
I hope this helps others.