I managed to do something in Construct 3 right now, and I hope it helps you.
From what I understand you want to select an object on the screen, and then move that object and only that object anywhere on the screen by touch.
Here you have a little example with two events.
In the image above you can see an object named Sprite2. This object is the same with the dog object from your example.
I added an instance variable "is_selected" to Sprite2 with the default value of 0.
I added the Touch to the project.
And as you can see from the image, when the Sprite2 object is tapped, is_selected takes the value of 1.
If now you tap anywhere on the screen and is_selected is 1, the Sprite 2 object will change it's position to where you tapped (Touch.X, Touch.Y).
Hope this help and if you have any more questions don't hesitate to ask them :D
Have a nice day.