[StartGames]

Вот что то на подобии CSS
#shipping_method_list input:checked ~ * .radio-input {color:red !important}

Т.е. если дочерный input отмечен checked тогда родительский элемент с класом .radio-input {color:red !important}

<div id="shipping_method_list">
					

						
							
								 
									<strong class="title nn">Доставка</strong>
								

								
									
									  <div class="radio-input radio active" id="su.flat.flat">
									    <label for="flat.flat">
									    
									      <input type="radio" name="shipping_method" value="flat.flat" id="flat.flat" checked="checked" data-refresh="5" class="styled"> 
									    
									    <span class="text">Доставка</span><span class="price">80 руб</span></label>
									  </div>
									
								
							
								 
									<strong class="title nn">Самовывоз</strong>
								

								
									
									  <div class="radio-input radio" id="su.pickup.pickup">
									    <label for="pickup.pickup">
									    
									      <input type="radio" name="shipping_method" value="pickup.pickup" id="pickup.pickup" data-refresh="5" class="styled"> 
									    
									    <span class="text">Самовывоз</span><span class="price">0 руб</span></label>
									  </div>
									
								
							
						
					
				</div>