The first big leap is considering experience to be a continuum from humans down to inorganic matter. This is stretching the meaning of 'experience'. If I walk on snow, does it experience deformation, or does it just deform?
The second leap is saying science only tells us what matter does and not "the intrinsic nature of matter: what matter is, in and of itself." I can't see how this gets you anywhere, you can say it's anything and it's self-satisfying.
The Hollywood ending really lost me. Let's just sweep this consciousness problem into a tiny tiny place and call it intrinsic: "So it turns out that there is a huge hole in our scientific story. The proposal of the panpsychist is to put consciousness in that hole. Consciousness, for the panpsychist, is the intrinsic nature of matter."