The definite article "the" shouldn't be included because we are talking about generalities, nothing specific. Portuguese rules regarding the use of articles differ from those of English.
You will also hear this idiomatic version: "How're things going?"
It is correct that when refering to generalities, like asking "how er you doing" there should NOT be a definite article in English, but how do we know that the Portuguese sentence only is supposed to refer to generalities? If used in context, where for example a group of people is working on a project - someone entering might ask "How are the things going" refering to that particular activity. Would you then use another construction to convey this meaning in Portuguese?
Although you would be understood, that is not a normal way to express yourself in English, although maybe once in a while, someone might say it like that, to be different. I would recommend sticking with How are things going? or How is it going? More informally, I'd say How's it going? Of course, these last phrases leave out the coisas, or things, but they mean the same thing.
In English, you can't say How the things are going? In a question, you must reverse the word order to How are things going? And we don't use the word "the" in that sentence. BTW, I also put How is it going?, and that was accepted, because it's also a normal way to talk in English.