This is a variation of a German phrase: Wie geht es? / Wie gehts du? / Wie geht es Ihnen? And they all mean: "How are you?"
The question is an inquiry into someone's state of being. To my understanding, it is similar in English to asking "How do you feel?"
The example most literally translates, by intention, to "How's it going?"
It IS grammatically correct English. AAVE is embedded into English vocabulary no matter what side of the pond you're on. America, England, even Aussies and Kiwis use AAVE. This is the 21st century. English, like all languages, has evolved. The language isn't wrong. The rules are. That's why they are ignored. I honesty can't think of one person ever asking me if I feel "well". "Are you doing good?, You all right?", or "How ya feelin'?" will almost always be heard before someone mutters "Are you doing well? Excelsior! Oh, pardon me whilst I remove my monocle"
The only problem here is that "Are you good?" is usually used in a different context. It is usually meant more like "Do you have everything you need?" or "Are we done here", whereas "Are you OK" is usually said when worried about how someone is doing, like if they appear to be hurting or just got in an accident. They are really 2 totally different questions, even though the difference is subtle.
You're right, there is a "mit" (or bei) in the full sentence, but almost no native German speaker actually says the full sentence anymore. In fact, they don't even say the "dir" part, since it's usually implied. This is a terrible example of dative case for beginners because it's essentially a colloquialism. Just learn it for the program and use "Wie geht's?" instead when speaking real German. (Unless you're being formal, then ask "Wie geht es Ihnen" and forget the "gut.")