NLT translation philosophy is the following (quote from NLT Bible Introduction, emphases mine):
The translators of the New Living Translation set out to render the message of the original texts of Scripture into clear, contemporary English. As they did so, they kept the concerns of both formal-equivalence and dynamic-equivalence in mind. On the one hand, they translated as simply and literally as possible when that approach yielded an accurate, clear, and natural English text. Many words and phrases were rendered literally and consistently into English, preserving essential literary and rhetorical devices, ancient metaphors, and word choices that give structure to the text and provide echoes of meaning from one passage to the next.
On the other hand, the translators rendered the message more dynamically when the literal rendering was hard to understand, was misleading, or yielded archaic or foreign wording. They clarified difficult metaphors and terms to aid in the reader’s understanding. The translators first worked to understand the meaning of the words and phrases in the ancient context; then they rendered the message into clear, natural English. Their goal was to be both faithful to the ancient texts and eminently readable. The result is a translation that is both exegetically accurate and idiomatically powerful.
The Greek word in Rom 8:38 that NLT translator renders as "demons" is frequently translated as either "ruler" or "principalities" (see here for comparison). What does "ruler" or "principalities" mean in contemporary (past 30 years) English? To a 6th grade reader (see here for reading level expected for various translations), "ruler" would mean governmental power like a King, President, and "principalities" would prompt a child to open a dictionary and find this (from Merriam Webster Dictionary):
1a: the state, office, or authority of a prince
b: the position or responsibilities of a principal (as of a school)
2: the territory or jurisdiction of a prince : the country that gives title to a prince
3 : principalities plural : an order of angels, see CELESTIAL HIERARCHY
But who is the ruler of this world that are also part of the order of angels? The New Testament is very clear who that is: it's the demons. See Bible Verses about Satan as ruler of this world. So the translation is quite faithful and easy to read.
Plus, it's easy to see how St. Paul wants to emphasize how God is more powerful than any elements of His creation using the rhetorical expression of opposites: death or life, angels or xxxxx, today or tomorrow. What's a good word for xxxxx ? There are good angels and there are bad angels. Paul already use "angels" for the good ones. So the most appropriate 6th grade word for contemporary English is .... demons of course! The plural form preserves the parallelism. Dan Brown book and movie Angels & Demons helps make that association too.
Therefore, "demons" is an obvious but still responsible choice suitable for the target audience: 6th grade reading level contemporary English.