Simply put, Williams rejects the tripartite interpretation of this verse as does Ryrie. Gen. 2:7 also seems to militate against any tripartite understanding of humanity. So those who believe in soul and body can make some kind of distinction between body, soul, and spirit or they can equate the soul with the human spirit. I've also seen theologians of Christendom define "spirit" as the vital force for humans and animals. But they try to argue that the human spirit differs from the spirit of animals.
Henry Alford on 1 Thessalonians 5:23:
τὸ πν. κ. ἡ ψυχ. κ. τὸ σῶμα] τὸ πνεῦμα is the spirit, the highest and distinctive part of man, the immortal and responsible soul, in our common parlance: ἡ ψυχή is the lower or animal soul, containing the passions and desires (αιτία κινήσεως ζωικῆς ζώων, Plato, Deff. p. 411), which we have in common with the brutes, but which in us is ennobled and drawn up by the πνεῦμα. That St. Paul had these distinctions in mind, is plain (against Jowett) from such places as 1 Corinthians 2:14. The spirit, that part whereby we are receptive of the Holy Spirit of God, is, in the unspiritual man, crushed down and subordinated to the animal soul (ψυχή): he therefore is called ψυχικὸς πνεῦμα μὴ ἔχων, Jude 1:19: see also note on 1 Cor. as above.