The power a government has over you, and the power your employer has over you, are totally different.
The government is legally authorized to separate you from your possessions, your freedom, and even your life in extremis. Your boss can't do any of that and if they try the government should stop them.
Some people believe democracy is what prevents the government from punishing you capriciously, or allowing corporations to just do whatever they want to you. So they are willing to die to defend it.
I would say traditional liberal ideals are closer to what they'd want to defend than democracy itself, and I don't 100% agree in either case, but I can see the point of view.