The polygon is has 4 ring parts, and your code is requesting a centroid for each ring part. The first ring part has 3 pairs of coordinates:
{
"geometry": {
"rings": [
[
[-9047616.7071, 3297677.1092999987],
[-9047617.2766, 3297676.960099999],
[-9047616.7071, 3297677.1092999987]
],
[
[-9047712.4177, 3297707.5879999995],
I'm not sure if the geometry is formed correctly, but I modified your code and ran the following in ArcMap's python window (10.5). I then converted the rings into geojson and created a polygon feature to get the coordinates of its centroid.
>>> for i in inputJSON['geometry']['rings']:
... coordinates = i
... try:
... polygon = arcpy.Polygon(arcpy.Array([arcpy.Point(*coords) for coords in coordinates]), inSr)
... pcent = arcpy.Point
... pcent = polygon.centroid
... print(pcent.X, pcent.Y)
... except:
... print("bad ring")
...
bad ring
(-9047688.632686786, 3297747.352303187)
(-9047607.857266191, 3297958.89263077)
(-9047509.45395274, 3297862.9346273225)
>>>
>>> coordinates = inputJSON['geometry']['rings']
... geojson_polygon = {"type": "Polygon", "coordinates" : coordinates }
... polygon = arcpy.AsShape(geojson_polygon)
...
... pcent = arcpy.Point
... pcent = polygon.centroid
...
... print pcent.X, pcent.Y
...
-9047510.96964 3297863.03471
If the polygon has only one ring, you may get the correct centroid. If it has multiple parts, you may be getting only the centroid of the first part.