I've read articles and books that discuss gut shots and have said that stomach matter and sometimes the lining itself can block a hole in the GI tract and the deer can heal and live fine afterwards. If that arrow caught the small intestine, which it could have possibly done in this case that wound is survivable from what I have read. The deer certainly looked no worse for wear in the video. I would think that if he were in bad shape it would have shown in his behavior that long after the hit.