I think you have to put geometryType parameter as shown below.
{"geometryType" : "esriGeometryPolygon",
"geometries" : [ {"rings":[[[5773777.49661869,2289563.95264293],[5773653.87350635,2289764.94666351],[5774526.1384941,2290309.87142669],[5774648.57525711,2290113.75075594],[5773777.49661869,2289563.95264293]]]}
]
}