Is it necessary to go through the search value?
Of course not. The Search input the easiest approach because the Search input is designed to filter records. Plus the server side processing is setup.
You selected the jQuery DataTable as the presentation design. In my opinion, the jQuery DataTable is a poor HTML design for displaying a directory structure. An unordered list is a much better representation and the approach I recommended around 5 months ago.
With that being said, it is up to you to come up with a design
As you suggested, the key to the code is to have created the two columns in the view; I think we can do something with that.
I have no idea what you are thinking... IsDirectory is currently being used in the jQuery DataTable to render HTML for a file or a directory.
The SQL View returns the relative path. It seems to me the relative path is the key. Write a service method that returns a distinct list of relative paths. Use this list in your HTML design. For example, a standard HTML select (dropdown). The user selects an option from the select which sets a column filter.
The jQuery DataTable has the ability to add column filters. Place the select in the path column header. See the openly published jQuery DataTable documentation.