Phrases such as this are called aphorisms, and while they may be commonly perceived to carry some truth and power, this is largely because they are well-known and often sound more insightful and scholarly than one's own thoughts or style of speech. Using aphorisms in this way, such as "a watched pot never boils" or "cheaters never prosper", would be considered an appeal to authority, namely the authority of the statement as "common sense" and the way in which it is delivered. While this may be true in some cases, aphorisms often communicate a simplistic or linear view of the world and human behaviors that don't necessarily match reality. Thus, I think "money is the root of all evil" would be an aphorism that I would fully expect someone to interpret from "The Devil and Tom Walker", but I think it's overly simplistic.
It was clear from the beginning of the story that Tom and his wife were miserly in all things, and that this poor personal character was what drove their other behaviors and their fates within the context of the story. We might expand the definition of money in this case to include "wealth", or just "possessions", but Tom would have had opportunities to use his new fortune for good and charitable works as well; instead he specifically devoted himself to evil as a part of the bargain. Saying "money is the root of all evil" is similar to saying "guns are responsible for killing people" rather than looking at the behaviors and motivations of the person pulling the trigger.
We should note that the phrase "money is the root of all evil" is taken from the Bible, and the full passage refers to the LOVE of money, not money itself. Complete and emotional devotion to anything is likely to lead to a deviance of moral character.