有几个问题。
这是一个工作版本，也处理点击按钮
我数出的选中的复选框数等于复选框总数。
我在tbody上加了个ID
我还使用ternaries

const $select_chk = $("#check");
const $table = $("#tbl")
const $checks = $table.find('input:checkbox')
const checkLength = $checks.length;
$table.on("click","tr", function(e) {
  if (!e.target.matches("[type=checkbox]")) { // if not a checkbox
    $(this).find("input:checkbox").click()    // click it anyway
  }  
  $select_chk.val(checkLength === $table.find('input:checkbox:checked').length ? "Unselect" : "Select");
});
$select_chk.on("click", function() { // we need function to get "this"
  const chk = this.value === "Select"; // check if text is select
  $checks.each(function() {
    this.checked = chk;
  });
  $select_chk.val(chk ? "Unselect" : "Select"); // toggle the text
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="button" id="check" value="Select" />
<table>
  <thead>
    <tr>
      <th></th>
      <th>Name</th>
      <th>Surname</th>
      <th>Gender</th>
      <th>Age</th>
    </tr>
  </thead>
  <tbody id="tbl">
    <tr>
      <td><input type="checkbox" /></td>
      <td>Cliff</td>
      <td>Deon</td>
      <td>Male</td>
      <td>52</td>
    </tr>
    <tr>
      <td><input type="checkbox" /></td>
      <td>Dennis</td>
      <td>Van Zyl</td>
      <td>Male</td>
      <td>25</td>
    </tr>
  </tbody>
</table>

//button click
$('#check').click(function(e) {
    if($(this).val()=='Select'){
        $('td input:checkbox').prop('checked',true);
        $(this).val('Unselect');
    }else{
         $('td input:checkbox').prop('checked',false);
         $(this).val('Select');
    }
});

//checkbox change
var $checkboxes = $('td input[type="checkbox"]');      
$checkboxes.change(function(){
    var countCheckedCheckboxes = $checkboxes.filter(':checked').length;
    if(countCheckedCheckboxes==$('td input[type="checkbox"]').length)
    {
        $('#check').val('Unselect');
    }
    else{
         $('#check').val('Select');
    }
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="button" id="check" value="Select" />
<table>
  <thead>
    <tr>
      <th></th>
      <th>Name</th>
      <th>Surname</th>
      <th>Gender</th>
      <th>Age</th>
    </tr>
  </thead>
  <tbody id="tbl">
    <tr>
      <td><input type="checkbox" /></td>
      <td>Cliff</td>
      <td>Deon</td>
      <td>Male</td>
      <td>52</td>
    </tr>
    <tr>
      <td><input type="checkbox" /></td>
      <td>Dennis</td>
      <td>Van Zyl</td>
      <td>Male</td>
      <td>25</td>
    </tr>
  </tbody>