The labels are not controlled by the Javascript API or REST API, but should be controlled by the mapping engine ArcGIS Server uses. If you zoom in the map further enough, the label should appear if you can see them in ArcMap or JS preview. You really have less control about it. One option you can do is to use the Maplex label engine in ArcMap to define the rule how the label should be drawn for short lines. Test it in ArcMap at each scale level your mapping site has, and publish it once you are satisfied with the result. But be aware that using Maplex engine may impact the site performance though.