Why would he mention the word "proper" in this context?

Native speaker’s answer
Rebecca
He mentions the word "proper" since there are multiple accents within New York, but only one that's genuinely a New York accent. Perhaps because other New York accents are influenced by other regions and accents. So there is only one New York accent that is "genuine" or "proper." Using "proper" before a noun is also a very British English thing to say! It sometimes functions as an intensifier. Ex: That's a proper British thing to do. Ex: I had a proper breakfast this morning => a real breakfast full of food Ex: That's a proper boat, right there. => intensifier