What is this type of flexible contact strip called?
That is called a zebra strip or Elastomeric_connector. 

It is made from silicone rubber with conductive carbon particles in them. This is used to make sure the connection between the PCB and glass is flexible, as both are neither thermally nor mechanically compatible at all. Also, as it doesn't rust or really react with anything galvanically at all it ensures a pretty good, albeint fairly high impedance, connection between the indium-tin-oxide or other connection material on the glass and the contacts on the PCB.