Second, calling someone rude is totally name-calling. Its insulting and humiliating. If someone calls you rude, its a conversation stopper. You feel condescended to. And if you talk about tone, the tone she said it to was so patronizing.
Saying that someone was being rude when they didn't have to be is not name-calling. She's characterizing his behaviour, but she does not say that 'rudeness' is a property of his person. It's a completely legitimate adjective to use, it is not offensive, it is not insulting or humiliating. It expresses that the one using the word is offended/insulted/humiliated. She did not get personal or angry, she called him on behaviour (without name-calling in any reasonable sense of the word) that is unbecoming of a restaurant setting and more appropriate for a bar.
Third, she OBEYS his request, but doesn't acknowledge his complaint. By saying he is rude, she implies he is asking too much. By not apologizing for the wait, she implies the wait was acceptable.
She is not obligated to bend over backwards for people. Her obeying the request signals that she is aware of their needs and that she intends to meet them. She acknowledges their concern that service is slow by informing them that they're having a busy day. Slow service is par for the course on busy days no matter where you work. An apology would have been cordial, but the lag could have went without saying.
Fourth, she had a condescending and patronizing tone the entire time. She said he "yelled" and he said "no I said excuse me." She didn't respond to that. He asked why was I being rude, she gave a bad answer, he called her on it and fucked off.
No she isn't. She's meek and visibly/audibly uncomfortable. She calls him out on his attitude, explains that they are having a busy day, and references an earlier incident in which he was yelling for her across the room (from the back of the restaurant to the front, presumably). He said he only said 'excuse me' but he could have been shouting it rudely, he could have been shouting it more than once, and he might have even said more. There's no need to take his word for it but even if you want to be naive and do precisely that, shouting across the room for a waitress is rude, and to be frank, idiotically indefensible on a busy day. People simply do not do this by and large on any scale. That he felt the need for it means he's entitled and impatient where all of the other patrons were perfectly capable of waiting during a busy day. She walked away because she didn't want to drag the dispute along. She had her opinion, he had his, and she saw no need to challenge him and argue about it even further when there were other customers and things to attend to. She did the right thing in walking away after addressing his rudeness.
<What customers and people want more than anything is acknowledgement. All she had to do was acknowledge they were very slow to pick up the plates, admit that they deserved better service.
Hey, maybe you're entitled like the people in this video. You don't have to project that onto everyone else like some unwritten law though. When I go out, I consider the day and the staff on hand. If things look busy I expect slow service. I stack my plates because I'm a fast eater and I like to be polite and make things a little easier for clean-up, not because I'm sitting there stewing in impatience. She did acknowledge the slow service, and she provided him with a reason why this was the case. An apology on top of that explanation would have been cordial, but once more, what with him yelling for her across the room and being rude during there interaction on camera, she probably didn't feel the need for picture perfect personality management. She was busy and stressed and had to deal with his bullshit among a room full of other customers who were presumably not choosing to act out like he was, so she called him out, addressed his needs, and gave him an explanation. She was calm and she avoided getting personal and insulting. She did not drag the interaction along and play into what him and his friends wanted (hence the camera). She did alright. It's time to let it go.