This excerpt is saying that the first five terms (the five beginning with smoking hot) can refer to food that is either spicy-hot (naturally hot, or hot because it has spices added to it) or to food that is temperature hot. But the term piping hot only refers to food that is temperature hot or 'hot out of the oven'.
I don't happen to agree with that statement, but as you can see, there is much discussion about the various phrases, with little consensus. Around the dinner table we will continue to say:
A: Wow, this food is hot!
B: Um, do you mean spicy-hot or hot-hot?
Person A will then pick one, or she could say she means both.
In all the vast vocabulary of English, we prefer to stick to one word, hot, to refer to both types of food. Well, at least it adds the occasional diversion to a meal.
You might be interested, if you haven't found them already, in these discussions on EL&U
How to say that food is hot (temperature) without the listener thinking that I mean “spicy”?
Difference between “spicy” and “hot”
I read the first one yesterday after I read your other question.
Compounding the issue, for some, is that spicy does not, or should not, even mean food that is naturally hot (or hot because certain spices have been added to it), because not all spices and/or herbs are hot (examples include cumin, cinnamon, mint, basil, oregano, garlic...there are dozens and dozens).