The authors consider $1 million (the difference between a person’s assets and liabilities) as the wealth threshold. In other words, millionaire is defined by the authors as Net Worth (including the home equity).
That said, I believe much of the authors' emphasis was more on the concept of wealth accumulation (saving and spending) than solely the acquisition of the eponymous number, as explained further by this cut and paste from Wikipedia:
UAWs versus PAWs[edit]
Under Accumulator of Wealth (UAW) is a name coined by the authors used to represent individuals who have a low net wealth compared to their income. A doctor earning $250,000 per year could be considered an "Under Accumulator of Wealth" if their net worth is low relative to lifetime earnings.[1] Take for example a 50-year-old doctor earning $250,000. According to the authors' formula he should be saving 10% yearly and should have about $1.25 million in net worth (50*250,000*10%). If their net worth is lower, they are an "Under Accumulator". The UAW style is based more on consumption of income rather than on the method of saving income.
A Prodigious Accumulator of Wealth (PAW) is the reciprocal of the more common UAW, accumulating usually well over one tenth of the product of the individual’s age and their realized pretax income.
The authors define an Average Accumulator of Wealth (AAW) as having a net worth equal to one-tenth their age multiplied by their current annual income from all sources. E.g., a 50-year-old person who over the past twelve months earned employment income of $45,000 and investment income of $5,000 should have an expected net worth of $250,000. An "Under Accumulator of Wealth (UAW)" would have half that amount, and a "Prodigious Accumulator of Wealth (PAW)" would have two times. This metric has been criticized since,[citation needed] for example, a 20-year-old making $50k a year should have a net worth of $100k to be considered an "average accumulator of wealth". That makes little sense since it would take a new graduate years of strong savings and investments to accumulate that amount. Critics[who?] further argue that formula fails to take into account compounding interest; younger people up to age 45 or so will generally have much less as a percentage of income than older wealth accumulators due to compounded growth.
Most of the millionaire households that they profiled did not have the extravagant lifestyles that most people would assume. This finding is backed up by surveys indicating how little these millionaire households have spent on such things as cars, watches, clothing, and other luxury products/services. Most importantly, the book gives a list of reasons for why these people managed to accumulate so much wealth (the top one being that "They live below their means"). The authors make a distinction between the 'Balance Sheet Affluent' (those with actual wealth, or high-net-worth) and the 'Income Affluent' (those with a high income, but little actual wealth, or low net-worth).
https://en.wikipedia.org/wiki/The_Millionaire_Next_Door