Berkhof's intent in those pages is to address people who might say, "Well, you understand the Scripture to mean one thing but I understand it to mean something else, and both are equally valid. I may understand it however I like." No, he says, there is a single right way to understand what a passage is saying. That's the "single sense" he has in mind.
He's NOT saying there's a single genre. The right way to understand the passage may be symbolically if the writer writes in a genre that uses symbolism. He's also NOT saying that the single right way to understand it can't lead to many valid points to be made, or have several applications, or have both a literal and symbolic/typical meaning, or have multiple fulfilments.