Data Tables plugin by Supsystic helps you not only to create and manage tables but also gives your site users ability to edit your table.
In order to allow only for logged in users to edit fields you need activate PRO version and follow these instruction:
- go to Settings tab -> Features
- click on Use Editable Fields for Logged In Users Only checkbox
- press on Save button
Also you can allows to use editable fields only for users with selected roles. For that click on Use Editable Fields for Current Roles field and select role you want (you can choose more than one). If there are no chosen roles – all logged in users will have ability to use the editable fields.