Update: Here's a version to try to avoid the memory errors from storing everything in a single list. Now, when the list has grown to the maximum possible size then the features will be added to the layer and the list cleared.

vl = QgsVectorLayer("Point?crs=", "temporary_points2", "memory")
vl.dataProvider().addAttributes([ QgsField("X_coord", QVariant.Int), QgsField("Y_coord", QVariant.Int), QgsField("Azimuth", QVariant.Int) ])

for row in range(0,rows):
   new_features = []
   for col in range(0,cols):
      rspnt = pixel2coord(col,row)
      fet = QgsFeature()
      fet.setGeometry(QgsGeometry.fromPoint(QgsPoint(rspnt[0], rspnt[1])))
      fet.initAttributes(3)
      fet.setAttribute(0, rspnt[0] )
      fet.setAttribute(1, rspnt[1])
      az = pntxy.azimuth(QgsPoint(rspnt[0], rspnt[1]))
      if az < 0.0:
         azim = 360 + az
      else:
         azim = az
      fet.setAttribute(2, azim)
      try:
         new_features.append(fet)
      except:
         vl.dataProvider().addFeatures( new_features )
         new_features = []

vl.dataProvider().addFeatures( new_features )
vl.updateExtents()
vl.updateFields()    
QgsMapLayerRegistry.instance().addMapLayers([vl])

it will be

Update: Here's a version to try to avoid the memory errors from storing everything in a single list. Now, the features are added once per row. It's not as fast as the above method, but less memory hungry:

vl = QgsVectorLayer("Point?crs=", "temporary_points2", "memory")
vl.dataProvider().addAttributes([ QgsField("X_coord", QVariant.Int), QgsField("Y_coord", QVariant.Int), QgsField("Azimuth", QVariant.Int) ])

for row in range(0,rows):
   new_features = []
   for col in range(0,cols):
      rspnt = pixel2coord(col,row)
      fet = QgsFeature()
      fet.setGeometry(QgsGeometry.fromPoint(QgsPoint(rspnt[0], rspnt[1])))
      fet.initAttributes(3)
      fet.setAttribute(0, rspnt[0] )
      fet.setAttribute(1, rspnt[1])
      az = pntxy.azimuth(QgsPoint(rspnt[0], rspnt[1]))
      if az < 0.0:
         azim = 360 + az
      else:
         azim = az
      fet.setAttribute(2, azim)
      new_features.append(fet)

   vl.dataProvider().addFeatures( new_features )
vl.updateExtents()
vl.updateFields()    
QgsMapLayerRegistry.instance().addMapLayers([vl])

Update: Here's a version to try to avoid the memory errors from storing everything in a single list. Now, when the list has grown to the maximum possible size then the features will be added to the layer and the list cleared.

vl = QgsVectorLayer("Point?crs=", "temporary_points2", "memory")
vl.dataProvider().addAttributes([ QgsField("X_coord", QVariant.Int), QgsField("Y_coord", QVariant.Int), QgsField("Azimuth", QVariant.Int) ])

for row in range(0,rows):
   new_features = []
   for col in range(0,cols):
      rspnt = pixel2coord(col,row)
      fet = QgsFeature()
      fet.setGeometry(QgsGeometry.fromPoint(QgsPoint(rspnt[0], rspnt[1])))
      fet.initAttributes(3)
      fet.setAttribute(0, rspnt[0] )
      fet.setAttribute(1, rspnt[1])
      az = pntxy.azimuth(QgsPoint(rspnt[0], rspnt[1]))
      if az < 0.0:
         azim = 360 + az
      else:
         azim = az
      fet.setAttribute(2, azim)
      try:
         new_features.append(fet)
      except:
         vl.dataProvider().addFeatures( new_features )
         new_features = []

vl.dataProvider().addFeatures( new_features )
vl.updateExtents()
vl.updateFields()    
QgsMapLayerRegistry.instance().addMapLayers([vl])

it will be