The baby starts searching for the breast. The mother guides him towards the nipple. The baby opens up fairly wide, but the mother does not bring the baby on as well as she could and the baby has a shallow latch. He should have more of the breast in his mouth.
The baby is mostly nibbling at first though there is an occasional pause in the movement of the chin (see other videos showing good drinking).
The mother starts compressing around 1 minute and 10 seconds, and the baby responds by starting to have pausing-types of sucks that indicate he is getting milk well.