"The Cloud Minders" is essentially about social inequality, and that's an issue that never really gets outdated, particularly today when the disparity between the very wealthy and powerful and the rest of us is an often discussed issue in tandem with views on the distribution of wealth.
The inhabitants of the cloud city Stratos are basically the top percentage of society who enjoy all the comforts and priviledges of their society while the Troglytes represent the rest of the population. The Troglytes do all the essential labour that allows the society to function yet are not allowed to share in much of the reward of their labours. The Stratos dwellers fulfill the role of government and overseers--the administrative part of society--reaping the fruits of the Troglytes' labour while sharing little if anything in return.
Interesting that Kirk and Spock initially liked and admired the city dwellers and their society and even in the end Kirk imposed pretty mild reforms rather than revolutionary changes ...