My question is, why did they use this idiom instead of just going to
The difference is a change in meaning. If the statement read:
In fact, she is going to dinner this evening
The meaning would be that the she was going to dinner, going implies travel, so the meaning here is that she is going to dinner somewhere, but the place has not been articulated in the statement.
Come[ing] around, in the context of the sentence means:
To visit someone in their home:
So the place of the dinner has been specified.
The meaning here is that she is going to the house of the narrator for dinner this evening.