Yes, SHOW not establish. Big difference.
Nobody is questioning the fact that the demons "believe" (mental assent) that "there is one God" but where in this passage does it say that demons believe or trust in Jesus Christ for salvation? The faith of demons is only "mental assent." Their trust and reliance is in Satan, as demonstrated by their rebellion in heaven and continuous evil works. The word "believe" can describe "mere mental assent," as in James 2:19 or also include "trust and reliance" in Christ for salvation, as in Acts 16:31. Saving belief is more than just an "intellectual acknowledgment" to the existence and historical facts about Christ. Saving belief trusts exclusively in Christ as the ALL-sufficient means of our salvation.
Faith without works is an empty profession of faith, not genuine faith which is evidenced by works. Notice closely that James does not say that Abraham's work of offering up Isaac on the altar resulted in God's accounting Abraham as righteous. No! The accounting of Abraham's faith as righteousness was made in Genesis 15:6, many years before his work of offering up Isaac recorded in Genesis 22. The work of Abraham did not have some kind of intrinsic merit to save his soul, but it proved or manifested the genuineness of his faith. This is the sense in which Abraham was justified by works, "shown to be righteous."
Faith made perfect by works means bring to maturity, carry to the end, to complete like love in 1 John 4:18. It doesn't mean that Abraham was finally saved based on his works. When Abraham performed the good work in Genesis 22; he fulfilled the expectations created by the pronouncement of his faith in Genesis 15:6. The scripture was fulfilled in vindicating or demonstrating that Abraham believed God and was accounted as righteous. Abraham was accounted as righteous because of his faith in Genesis 15:6 long before he offered up Isaac on the altar and demonstrated the reality of his faith in Genesis 22.
They are not both united as the root of salvation. Faith is the root and good works are the fruit and we are saved FOR good works, NOT BY good works (Ephesians 2:8-10).