A sharp broadhead is what kills an animal. Everything else is just a delivery system. Properly tuning your setup and developing good form help to ensure accurate delivery, but there are quite a few methods of doing those things that all yield good results.
My dad has been a bowhunter since I was a small child, but has always been a compound guy. When he started out, he got some help and guidance from an older guy that had hunted with both recurves and compounds. His first piece of advice was this: "the key to bowhunting is getting them close". In spite of what his equipment is "capable" of, my dad has limited over 90% of his shots to 15 yards or less. He passed that advice on to me, and in all the years that I hunted with a compound, I only shot once at an animal over 15 yards. When I took up trad, that philosophy fit perfectly with this style of hunting.
To answer the original post, in my opinion, the most important things to being a traditional bowhunter are getting them close, and having a good quality sharp broadhead that you can deliver accurately within that close range. .