Guys, How do you deal with that guy at work that is not your boss, but he is a boss, and wants to be bossy with you?

It depends on the culture of your workplace. Some workplaces allow anyone higher up than you to be bossy. Some workplaces only allow your own boss to be bossy with you. Observe how your colleagues act in similar scenarios. However, do have a think before you raise this sort of issue in conversations with colleagues or your boss, as this may not be effective, if it is not appropriate to talk about this with others in your workplace. Maybe seek the advice of your friends and family, who will know more about your specific job than I do.

There are people like this all over the place. I've been able to successfully head them off by telling them to coordinate his deliverable schedule with my boss, get the bosses talking to each other. Because if the real boss knows that the fake boss is threatening his timelines, he's liable to allow me to tell the fake boss to screw off whenever I want.

it's kind of like the military, you have someone over you, maybe a corporal, maybe a sgt but they also have someone over them who in turn could actually have some control over your actions
ie. if you were doing something not accepted, and anyone with a higher rank saw you do it they have every right to give you correction or instructions
so your not immediate boss can determine your actions within the company if he sees you doing something that is not accepted by the company

If he is a supervisor, not your supervisor, but a person who is above you in the company, you follow what they say unless you goes against what your job is. Then you tell your supervisor and see if they want you to do it, and if they do then do it.

If he's my boss's boss, then I treat him/her deferentially. Otherwise I ignore him/her.

If he's a boss, I do what he says. If what he says conflicts with what my direct boss says, then I ask my boss which one I should do.

Let them be bossy, nothing you can do about it. Just do your job the best you can.