I am not sure how those specific games were built, but if I wanted to make something similar I would not actually have my character move horizontally once shot from the mouse, all I would do is scroll the background to have the appearance of movement. Then I would make the art for the background just scroll horizontally in the opposite direction you want the character to travel until the object that was shot has finally stopped on the ground. The scroll would just loop infinitely.
For the object to have that appearance of vertical bounce, you could probably use the physics plugin and just have increasing gravity while the object is in the air. Again, the object would never move horizontally, just vertically, the illusion of horizontal movement would come from the background scrolling.
The infinite runner template is a good starting point for this system. If you can't get the template to work you can probably find Construct 2/3 infinite runner tutorials on youtube that will help you recreate it.
I hope that is of some help to you.