Would a Chinook helicopter fly better with contra-rotating along with counter-rotating propellers?
No.  The RC model there is using counter-rotating rotors because the upper rotor with the stabilizer bar has a specific function that makes the model controllable in the first place.

The Chinook already benefits from built-in anti-torque control so that would be a waste of time and oodles of money on the real one.

Fun fact about the Chinook: it can climb better, and fly on less power overall, going sideways. Both rotors are able to bite clean air, achieving translational lift, when going sideways.  When going forward, the rear rotor has to cope with the wake of the front one.