One approach to the problem you're facing, that of showing the number of the table-row element can be solved using CSS, with the following rules:
tbody {
  counter-reset: rownumber;
}
tr {
  counter-increment: rownumber;
}
td:first-child::before {
  content: counter(rownumber, decimal);
}
The above defines the counter, rownumber and has it be reset via the <tbody> element; so if rows are appended over multiple <tbody> elements then the <tr> descendants of each will be numbered independently of each other. If you'd prefer a continuous count of all <tr> elements then simply move the counter-reset rule up to the <table> element, or to any other (ideally the closest possible) ancestor within which you require a cumulative count.
This counter is incremented, by 1, in each <tr> element, and then shown in the ::before pseudo-element of the first <td> child of each <tr>. The second argument to counter() is the type of counter you wish to use (see this answer for the (current) possible options: https://stackoverflow.com/a/16943843/82548 (disclaimer: it's one of my answers, the second Snippet will allow you to see the results of different counter types).
So, that part covered I've also rewritten – I'd like to say revised or refactored, but that would be, at best, an understatement – your posted code into the following function. Code explained in the comments:
// a named function to call:
function addRow() {
  // using 'let' to declare variables, this is mostly a
  // matter of personal preference in this case, and if
  // 'let' is unavailable to you, or your users, can be
  // replaced with 'var'.
  // here we define a 'details' Object to hold the
  // variables from the <input> elements we find
  // later:
  let details = {},
  // we use document.querySelector() to retrieve the first,
  // if any, elements matching the supplied CSS selector;
  // this is the element to which new content will be added:
    target = document.querySelector('#myTable tbody'),
  // and again we use document.querySelector() to find the
  // element we'll be cloning in order to append the new
  // new content:
    source = document.querySelector('#myTable tfoot tr.template')
      // we pass (Boolean) true as an argument in order to copy
      // the descendants of the cloned node as well as the node
      // itself:
      .cloneNode(true),
    // here we use Array.from() to convert the Array-like
    // HTMLCollection returned from document.querySelectorAll()
    // (which retrieves all the elements which match the
    // supplied CSS selector) into an Array:
    inputs = Array.from(
      document.querySelectorAll('form label input')
    );
  // we make use of the Array, via Array methods such as,
  // here, Array.prototype.forEach(), which iterates over
  // the elements of the Array:
  inputs.forEach(
    // using an Arrow function, rather than the traditional
    // anonymous function; here 'input' refers to the current
    // Array element of the Array of <input> elements over
    // which we're iterating.
    // here we update the details Object, by adding a new
    // key (details[input.id]) and setting the value of that
    // key to the value (input.value) held in the <input>:
    input => details[input.id] = input.value
  );
  // here we convert the Array-like NodeList of child-
  // elements of the source (the <tr> element we cloned
  // earlier) into an Array, again using Array.from, and
  // then iterating over those elements using, again,
  // Array.prototype.forEach():
  Array.from(source.children).forEach(
    // in this Arrow function we're naming the
    // current Array-element 'cell', the name is
    // purely a personal choice, and can be almost
    // anything, so long as it's valid in JavaScript.
    // here we set the text-content of the current
    // cell (<td> element) to be equivalent to the
    // value held in the details Object at the same
    // custom data-* attribute, here data-from, as
    // the current <td> (details.cell.dataset.from);
    // if there is no key of that name, we set the
    // text to an empty String (''):
    cell => cell.textContent = details[cell.dataset.from] || ''
  );
  // we append the newly modified <tr> element to
  // the target element (the <tbody>):
  target.appendChild(source);
  // and here we iterate over the <input> elements:
  inputs.forEach(
    // and set the value of each <input> back to
    // its default value, the value it held on
    // page-load in order to save the user having
    // to first delete existing content before
    // entering new content to add:
    input => input.value = input.defaultValue
  );
}
document.querySelector('#addRow').addEventListener('click', addRow);
function addRow() {
  let details = {},
    target = document.querySelector('#myTable tbody'),
    source = document.querySelector('#myTable tfoot tr.template')
    .cloneNode(true),
    inputs = Array.from(
      document.querySelectorAll('form label input')
    );
  inputs.forEach(
    input => details[input.id] = input.value
  );
  Array.from(source.children).forEach(
    cell => cell.textContent = details[cell.dataset.from] || ''
  );
  target.appendChild(source);
  inputs.forEach(
    input => input.value = input.defaultValue
  );
}
document.querySelector('#addRow').addEventListener('click', addRow);
body {
  box-sizing: border-box;
}
label {
  display: block;
  width: 55%;
  overflow: hidden;
  margin: 0 0 0.5em 0;
}
table {
  table-layout: fixed;
  width: 90%;
  margin: 1em auto;
  border-collapse: collapse;
}
label input {
  width: 50%;
  float: right;
}
th,
td {
  border-left: 1px solid #000;
  border-bottom: 1px solid #000;
  line-height: 2em;
  height: 2em;
}
th {
  text-align: center;
}
th::after {
  content: ': ';
}
td:first-child,
th:first-child {
  border-left-color: transparent;
}
tbody {
  counter-reset: rownumber;
}
tbody tr {
  counter-increment: rownumber;
}
tbody td:first-child::before {
  content: counter(rownumber, decimal);
}
tfoot tr.template {
  display: none;
}
<form action="#">
  <fieldset>
    <legend>Add new details:</legend>
    <label>FirstName
      <input type="text" id="firstN" />
    </label>
    <label>LastName
      <input type="text" id="lastN" />
    </label>
    <label>Points
      <input type="text" id="pnt" />
    </label>
    <button type="button" id="addRow">Add</button>
  </fieldset>
</form>
<table id="myTable">
  <thead>
    <tr>
      <th>Rownumber</th>
      <th>FirstName</th>
      <th>LastName</th>
      <th>Points</th>
    </tr>
  </thead>
  <tfoot>
    <tr class="template">
      <td></td>
      <td data-from="firstN"></td>
      <td data-from="lastN"></td>
      <td data-from="pnt"></td>
    </tr>
  </tfoot>
  <tbody>
  </tbody>
</table>
 
 
JS Fiddle demo.
References: