Why does this GPS approach say "RADAR REQUIRED"?
The immediate reason seems to be that for RNAV approaches that start at an IF (Intermediate Fix) - not an IAF (Initial Approach Fix) - radar is required per the ATC orders (4-8-1h):


  issue approach clearance [...] only after the aircraft is:  
  
  
  Established on a heading or course direct to the IF at an angle not greater than 90 degrees, provided the following conditions are met:
  
  
  [...]
  
  (b) Radar monitoring is provided to the IF.
  (c) The SIAP must identify the intermediate fix with the letters “IF.”


The RNAV 26 approach that you mentioned does have an IAF, so according to the same rules radar isn't always required for it.

You might now ask, why is radar required for RNAV approaches that start at an IF? Because, it doesn't have an IAF. 

The next question is why doesn't it have an IAF? Probably because of higher terrain north of the approach corridor? Or maybe (as per @Jonathan Walter's answer) there is sufficient Radar coverage to vector to the IF, so it doesn't need an IAF.