Show contextual link for each node on node listing page
If you are building the node listing page using views, you can


Enable contextual links module.
In the fields for the listing, add a field 'Content : Edit Link'. Then select Exclude from display.
Add a Global : Contextual Links field. In the field settings, check the edit link field. 
You should be good to go.
You can also add additional field in the context menu if you want.