What is a Cruise Captain?
According to the discussion here it seems a "cruise captain" is the captain who flies only during the cruise stage of flight. You can find a job listing for a "cruise captain" here but it does not elaborate much on the duties. To act as the pilot in command (at least by FAA regs) they would have to be current, and type certified in the aircraft in question. It seems the term is more a turn of phrase and the regulations are not any different for a cruise captain. On very long haul flights that may require 3 full crews, there will be a crew in the middle section of the flight that never sees takeoff or landing from the cockpit. 

The report you have linked in the comments defines cruise captain in the foot note on page 3. 


  Cruise Captain in this report refers to a pilot certificated as cruise
  captain by the Malaysian Aviation Authority, and is qualified by the
  company to act as PIC during cruise only and who was engaged in the
  operation of the aircraft.


It sounds like "Cruise Captain" in this case is a Malaysian Aviation Authority term (although it may apply elsewhere as well). I am looking for the actual regulation that defines it but have not yet come across them.