He was brought to the hospital where they did an x-ray of the hand and it showed no bone injury. Arrow was then cut with a saw, lidocaine was injected both on the entry and the exit site to numb the area and the arrow was gently pulled out. The hand was then soaked in a dilute iodine solution. On examination there apeared to be no major neurovascular damage besides a slight numbness of the inside of the finger. He was given oral antibiotics an pain medicine.
This is a fairly common injury to see when an inexperienced archer uses a bow whose draw length is too short for the archer. They pull back too far, the tip of the arrow comes off the rest and slips toward their hand as they let go, and the arrow pierces their hand. Sometimes the carbon fiber splinters and it's a much bigger mess.
My guess is using too short of an arrow. When he pulled the bow taught the arrow slipped from the rest, angling towards his hand. This appears to be his left hand which is the same one that most people grip the bow with.