The word "soul" in Psalm 72:13 (KJV) is the Hebrew word נָ֫פֶשׁ (nephesh - Strong's H5315), the same word that is found in Genesis 2:7, which says:
And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
So, the "soul", as far as the Old Testament is concerned, is something that one IS - a collection of atoms (the dust of the ground). To become a LIVING soul, the collection of atoms had to be animated by the breath of God נִשְׁמַ֣ת (neshamah - Strong's H5397. The breath of God was needed so that the collection of atoms would want (desire) to move - all on its own.
Things that have no neshamah, are inert, i.e. they have no power within themselves to move from a state of rest, or from a state of fixed motion - they must be "coerced" from one state to another.
Actually, none of the versions you mention have it right. It should read:
יחס | על־ | דל | ואביון | ונפשות | אביונים | יושיע׃
VERB | ADJ | NOUN | ADJ | ADJ | (prep) | (verb)
shall | | | (the) | (the) | | shall have
save | needy | soul | needy | poor | on | compassion
Which, I contend, gives:
He shall have compassion on the poor and the needy, and shall save the needy souls.
I put the parts of speech in so you can see this for yourself. The adjective "needy" modifies the noun "souls", so it's not "the souls of the needy", but "the needy souls"
I think translators have been influenced by the presiding philosophies of their day, in particular Greek philosophy, and they think of the notions of "soul" and "spirit" as being synonymous. They aren't, of course.
For those who might be struggling with the regular use of the adjective here, please present an answer to the question being asked. In your answer give some thought to the claim that it should be translated in any other way than what is natural.
For example, in English we might reconfigure the sentence, "The young woman had blue eyes.", as "The young woman had eyes of blue", but never as "The young woman had the blue of the eyes". That is what the translators are doing in this instance. They are allowing their bias towards the idea that "soul" and "spirit" are synonymous, from whatever source it comes, to dictate what should be a straight forward translation of the text.