I did not go back for a second look, but the first shot looked a little bit back to me. Looked like liver/diaphragm, perhaps one lung. That deer did what I have seen every deer do in that condition. Lay down, get up, lay down, get up lay down. Without an explanation of the wound channel it is only speculation, but that deer likely would not have gone more than a couple hundred yards no matter what unless pushed, and might have taken several hours to expire without a follow up shot. Pushing wounded deer is likely the biggest and dumbest reason people lose deer that they should be able to recover.
How would I track this deer? Start by paying very close attention to where the arrow hit, exactly where the deer runs off to and exactly the last place I saw it. Replay all of it over and over in my head for the next hour while I keep looking and listening. If I was certain that I hit that deer where he did, I wait many hours before taking up the trail. Depending on how far I think the deer was when I last saw it, I might look for blood, my arrow, hair, etc. where he was standing when hit if all was quiet for an hour or so. Then sneak the fuck out and come back with help 6-8 hours later. Maybe wait overnight if weather permits. Patience and discipline required.
