Generally people who want to make home video want to know the name of the app.

There's an included effect in After Effects called CC Simple Wire Removal.  You track both ends of a wire and it blurs it out (sort of)

JakeInMotion has a video talking you through it:

https://www.youtube.com/watch?v=ALAoNGXvLC4

For the shot in question though, they appear quite thick wires and you might need to resort to the Rotobrush instead.