Does PostgreSQL/PostGIS use R-Tree or R*-Tree?
I'm not sure what is the vanilla R-Tree but there is internal citations inside the source file you linked.  Also, the R-Tree inside of PostGIS is directly copied from PostgreSQL with these minor modifications (as in the FAQ),


  Why aren't PostgreSQL R-Tree indexes supported?
  
  Early versions of PostGIS used the PostgreSQL R-Tree indexes. However,
  PostgreSQL R-Trees have been completely discarded since version 0.6,
  and spatial indexing is provided with an R-Tree-over-GiST scheme.
  
  Our tests have shown search speed for native R-Tree and GiST to be
  comparable. Native PostgreSQL R-Trees have two limitations which make
  them undesirable for use with GIS features (note that these
  limitations are due to the current PostgreSQL native R-Tree
  implementation, not the R-Tree concept in general):
  
  
  R-Tree indexes in PostgreSQL cannot handle features which are larger than 8K in size. GiST indexes can, using the "lossy" trick of substituting the bounding box for the feature itself.
  R-Tree indexes in PostgreSQL are not "null safe", so building an index on a geometry column which contains null geometries will fail. [GiST indexes are null-safe]