If they a quit their job because they have a few extra million then they were working class (ie they needed to work to survive).
It's not all black and white.
Apparently that’s not enough when you have expensive tastes.
You're also correct that traditionally the proletariat (the working class) were those who sold their labour. By a very strict definition, anyone who earns a wage is working class and that would include CEOs (as you are doing explicitly). That definition is deficient and doesn't relate to reality.
Traditionally, the bourgeoisie were the class or classes who employed the workers. The capitalists own the capital and capital goods (means of production) that are used in industry. The petit bourgeoisie are those who own small businesses, such as shopkeepers or lawyers. They were middle class because they were neither working class nor part of the nobility.
Today many companies are publicly held. By this, I mean that stakes in the company are sold publicly. Many companies are also part-owned by the public in the sense of state ownership. This kind of relationship would falsely suppose that members of the working class are members of the bourgeoisie. You agree that ownership doesn't exactly determine class since your criterion is the selling of time or labour.
Those today who have power over the factors of production are very often employed when previously they employed themselves. You call these people working class. I find that very bizarre.
I believe that a managing director of an investment bank is a person who represents capital absolutely. Their job is to head an organisation whose aim is to manage capital and to generate or bring in capital in the process. To identify this person with a factory worker is confused.
I think you're trying to play around with definitions because you think there's a moral component to class.
Money is power, so the man is those on the top floors of institutes dealing with large amounts of money and having gala evenings with politicians and CEOs.
That's who the working class person making minimum wage that was just made redundant actually works for.
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Saying that the investor bank executive is working class because he needs to pay his rent is bollocks.
Sorry, it's your definition that is wrong. "Working class" doesn't mean "category of people that work."
"When used non-academically in the United States, [...] it often refers to a section of society dependent on physical labour, especially when compensated with an hourly wage. For example, the working class is loosely defined as those without college degrees. Working-class occupations are then categorized into four groups: unskilled labourers, artisans, outworkers, and factory workers."