Could the Boeing 787-9 near vertical takeoff demonstration be performed by Airbus A350 aircraft? I am an aviation enthusiast. A couple of months back I came to know about the difference between piloting Boeing and Airbus planes here.

What are the main differences piloting Boeing vs. Airbus aircraft?

The very first comparison says this:


  Boeing trusts more the pilots: they can supersede the autopilots
  commands by exerting enough force on the controls
  
  Airbus trusts more the autopilot: if the system is fully functional it
  will always have priority over the pilots (but they still have room
  for "non-standard" maneuvers, e.g. commanding bank angles beteween 33°
  and 60°)


Also another answer stated this:


  Airbus aircraft limit pilots' capabilities in situations that require
  extreme action to be taken; the computer may prevent the pilot from
  pushing the plane past its safe ranges, which could be necessary in
  case of an emergency.
  
  Boeing aircraft leave ultimate control mostly to the pilot.


Now relating the above points with the recent near vertical take off by Boeing 787-9 in the Paris air show 2015:



Is this near vertical take off is an example that "Boeing aircraft leave ultimate control mostly to the pilot"? If Airbus aircraft trust the autopilot more, would they allow this type of takeoff as it is done by pilot by pushing the engines to extreme? Also, is it some kind of mockery by Boeing to Airbus?

For those who haven't yet watched the video, here is the link:
No.

Firstly, as a comment noted, the takeoff was hardly "near vertical", the camera angle makes it look so. The takeoff angle in the video certainly is much steeper than a normal one, but Airbus aircraft are more than capable of doing the same - in fact an A350 did very much the same thing at the Paris Air Show. 

The notion that an Airbus doesn't let the pilots have complete control is a little bit misleading. I'm not going to go into too much detail in this question, but what most people are referring to when they say that is the Alpha Protection system. This system kicks in when the aircraft is at extreme angles of attack. For example, if an aircraft is about to stall, it will not let the pilot pull the nose up. In any plausible situation the pilot would not want to raise the nose anyway, yet we have seen accidents such as Colgan 3407 where the pilot did exactly that (and, also AF447, however the system was disabled in that crash). 

In summary, the Airbus system pretty much only prevents pilot actions that are dangerous (OK it is more complex than that, and the Boeing design has benefits too, but..). Back to your question, why does the Airbus system also allow such a steep takeoff? Because only the attitude was high, but the angle of attack was still within normal limits. These takeoffs are possible on lightly loaded aircraft with engines near full power.