In no way does this lead to nihilism.
Of course not! Because is already nihilism. You know that! You're an intelligent man!
Sam Harris supports eliminativism and that means consciousness is just an illusion. It's not just elimination about some especific spooky sense of transcendence but the whole Self is just an illusion. In this talk he's clearing refuting reducionism and promoting eliminativism.
Don't fool yourself cofty. You know by killing God you kill yourself too. If God is an illusion so are you. There's no point arguing about "differences" between illusions.
I know in your mind you'll never accept that you are just an illusion, and this will bring a lot of pain in your soul.
I know that not so deep in your mind, when you think about your own death, automatically comes a steady sensation that someway somehow clinical death is not the end.
Don't let bad experiences with false prophets (JW's and Pentecostals) fill your soul with revolt against God.