Chalmers here begins, "Panpsychism, taken literally, is the doctrine that everything has a mind", which agrees with the general use. Then he redefines the word to mean "the thesis that some fundamental physical entities have mental states".

His "taken literally" qualification implies that the universal quantification of the "pan-" prefix is usually limited in some unspecified way, making his redefinition seem less of a break, but I do not think that the SEP article on panpsychism supports a limitation as drastic as the one he is making. His "some" could accommodate consciousness being present only in humans; no historical use of "panpsychism" in the SEP article can.

So you did not misunderstand Chalmers, but Chalmers would better have picked a different word. I think "psychism" fits the bill.

If some entities have a soul and others do not, there remains the same question as for the materialistic doctrine: why these and not those, and how does it work? We then get "emergent psychism", where what emerges from unensouled matter is not the right configuration to be a soul, but the right configuration to have a soul. And if answers to these questions are found, we end up with materialist psychism, with an expanded set of materials. At which point materialist philosophers can point out that this was materialism all along.