It doesn't look like there's any need to open those pdfs in the first place, since all your script is doing is putting a filename in each row of :File Name.
Names Default to Here( 1 );
//point to file directory
path = Pick Directory( "Select Directory Containing Data Files" );
//Gets the list of files in the selected file folder
file_list = Files In Directory( path );
// Create beginnings of output data table
dtFinal = New Table( "Final", New Column( "File Name", Character ) );
//i=0;open file
nfile_list = N Items( file_list );
For( i = 1, i <= nfile_list, i += 1,
//Set Current Directory( dir_DirectoryPath );
//dt = Open( path || file_list[i], );
// Add information to Final data table
dtFinal << add rows( 1 );
dtFinal:File Name[N Rows( dtFinal )] = file_list[i];
);
But you could do it even quicker and more efficiently.
Names Default To Here( 1 );
path = Pick Directory( "Select Directory Containing Data Files" );
dtFinal = New Table( "Final", New Column( "File Name", Character, Set Values( Files In Directory( path ) ) ) );