You don't need to buy the park entrance.. they offer it there but there's no need. Also remember that this is a domestic flight, so there is no immigration. Having said that there is a control when you leave Santiago and again when you leave Easter Island in order to prevent people overstaying on the island. Before this control you need to fill a form where you need to declare where you'll be staying. You can find the form here: https://ingresorapanui.interior.gob.cl/# Timewise, there should be no problem to land, exit the terminal, control, security and board as long as you have your boarding pass on your phone.