An ArcGISDynamicMapServiceLayer is used to display a map service in a JS API app and is collection of one or more layers. As a result, dynamic layers don't have a geometry type but individual layers in the map service do have a geometry type.
We have a sample showing how to retrieve individual layer info. To get geometry type, you would use the same code shown in that sample but instead of pulling out field info, you'd pull out the layer's geometry type.