You have clearly never experienced extreme pain. The last time I suffered a severe shoulder dislocation was almost like an out-of-body experience. The pain overwhelmed the ability to form coherent thoughts, it was like an electrical storm in my brain. The intuitive motor system took complete control as I writhed around, limbs flinging in random directions. I heard someone scream at the top of his lungs, and only afterwards realised that it was me.
Pain absolutely does have a physical component, and it is not something you can overcome just by practicing meditation. Though, I’m not saying that doesn’t help in some scenarios.
If influential means influencing game design / the industry, inspiring other creators by demonstrating novel ideas, I’d probably have to say Doom or Half-Life. Doom really showed what an FPS could be and kicked off such a dominant genre. Half-Life introduced immersive storytelling that greatly influenced FPS and non-FPS games.