How to make datatable row or cell clickable?

To activate click on cell you must use a delegated event handler – this will work on any dataTable :

$('.dataTable').on('click', 'tbody td', function() {

  //get textContent of the TD
  console.log('TD cell textContent : ', this.textContent)

  //get the value of the TD using the API 
  console.log('value by API : ', table.cell({ row: this.parentNode.rowIndex, column : this.cellIndex }).data());
})

Retrieving data of a clicked row can be done by

$('.dataTable').on('click', 'tbody tr', function() {
  console.log('API row values : ', table.row(this).data());
})

If you want to send row content via AJAX you should transform the array to an object, and then include it as data :

$('.dataTable').on('click', 'tbody tr', function() {
  var data = table.row(this).data().map(function(item, index) {
     var r = {}; r['col'+index]=item; return r;
  })
  //now use AJAX with data, which is on the form [ { col1 : value, col2: value ..}]
  $.ajax({
    data: data,
    url: url,
    success: function(response) {
       ...
    }
})

If you just want a plain link in a cell with target: _blank you can use render :

columns: [
  { title: "Patient ID", class: "center", render: function(data, type, full, meta) {
     return '<a href="https://stackoverflow.com/questions/35547647/showdata/id?"+data+'" target=_blank>Show patient</a>'
  }
},