Is this type of ground wire connection NEC compliant?
Simply twisting is not enough. You need a mechanical connection as well. Wire nut, crimp, etc.

NEC


  110.14 Electrical Connections
  
  Because of different characteristics of dissimilar metals, devices
  such as pressure terminal or pressure splicing connectors and
  soldering lugs shall be identified for the material of the conductor
  and shall be properly installed and used. Conductors of dissimilar
  metals shall not be intermixed in a terminal or splicing connector
  where physical contact occurs between dissimilar conductors (such as
  copper and aluminum, copper and copper-clad aluminum, or aluminum and
  copper-clad aluminum), unless the device is identified for the purpose
  and conditions of use. Materials such as solder, fluxes, inhibitors,
  and compounds, where employed, shall be suitable for the use and shall
  be of a type that will not adversely affect the conductors,
  installation, or equipment.
  
  (B) Splices.
  
  Conductors shall be spliced or joined with splicing devices identified
  for the use or by brazing, welding, or soldering with a fusible metal
  or alloy. Soldered splices shall first be spliced or joined so as to
  be mechanically and electrically secure without solder and then be
  soldered. All splices and joints and the free ends of conductors shall
  be covered with an insulation equivalent to that of the conductors or
  with an insulating device identified for the purpose.
  
  Wire connectors or splicing means installed on conductors for direct
  burial shall be listed for such use.