Adapted views-view-table template for Twig in Drupal 7. Approach would not be appropriate for D8 (or necessary).

gistfile1.php

<?php
// Preprocess
function minim_preprocess_views_view_table(&$variables) {
  if (!empty($variables['header'])) {
    $variables['headers_rendered'] = '';
    foreach ($variables['header'] as $field => $label) {
      $variables['headers_rendered'] .= "<th class='" . $variables['header_classes'][$field] . "'>" . $label . "</th>";
    }
  }
  if (!empty($variables['rows'])) {
    $variables['rows_rendered'] = '';
    foreach ($variables['rows'] as $row_count => $row) {
      if (!empty($variables['row_classes'][$row_count])) {
        $variables['rows_rendered'] .= "<tr class='" . implode(' ', $variables['row_classes'][$row_count]) . "'>";
      }
      else {
        $variables['rows_rendered'] .= "<tr>";
      }
      foreach ($row as $field => $content) {
        if (!empty($variables['field_classes'][$field][$row_count])) {
          $variables['rows_rendered'] .= "<td class='" . $variables['field_classes'][$field][$row_count] . "'" . drupal_attributes($variables['field_attributes'][$field][$row_count]) .">" . $content . "</td>";
        }
        else {
          $variables['rows_rendered'] .= "<td " . drupal_attributes($variables['field_attributes'][$field][$row_count]) . ">" .  $content . "</td>";
        }
      }
      $variables['rows_rendered'] .= "</tr>";
    }
  }
}


// Template
<table class="{{classes}}" {{attributes}}>
  {% if title or caption %}
    <caption>{{caption}}{{title}}</caption>
  {% endif %}
  {% if headers_rendered  %}
    <thead>
      <tr>
        {{ headers_rendered }}
      </tr>
    </thead>
  {% endif %}
  {% if rows_rendered %}
    <tbody>
      {{ rows_rendered }}
    </tbody>
  {% endif %}
</table>