"Give me more money or I leave" is negotiation (specifically, an ultimatum), and is a perfectly legitimate tactic. Standing up and leaving is throwing a tantrum (or a last resort if the ultimatum fails) - doing so without first telling the other party your problem and giving them a chance to fix it is completely unprofessional.
WRT your definition of blackmail, I'm getting "the action, treated as a criminal offense, of demanding money from a person in return for not revealing compromising or injurious information about that person." It's a VERY specific term having to do with hidden information.
What you cited seems closer to the definition of extortion ("the practice of obtaining something, especially money, through force or threats"), but frankly, as long as what you're threatening to do is legal, that's business.
Your relationship with your employer is first and foremost a business relationship - they are not your best friend, your family, or your surrogate father. You have no obligation to play nice with their feelings.
I understand your impulse to not give in to an employee that demands like this, but you need to drop the moralizing BS - what you're saying is "they know what they're worth and I can't afford to pay that, so I'll only hire employees who don't know what they're worth". Sound accurate?