Here is an older workspace reading json from our google geocoder (we have enterprise license to do this).
The process is simple it sends a request out to the service [most api's will return json or xml] which returns the json file which then will be processed and reformatted
Note:we had to use a decelerator transformer because FME was processing the inputs too fast to the api service (blocks if too fast)
0.5 second delay worked for get the responses back.
Update you need a creator first with a Null value (you populate this later)
httpcaller (fetcher) is the json file your are calling from the web
JSONfragmentor (exploder) will get the json info
You will need to break the response up into attributes then you can create points, lines, polygons from the data you have extracted.
this is the file it is retrieving in json format
Update2 your data is in GeoJSON (not json) use the GeoJSON reader in FME 2015