This is called appeal to emotion, argumentum ad passiones: "manipulation of the recipient's emotions in order to win an argument, especially in the absence of factual evidence". In other words, dispassionate reasoning (in this case, about rape) is replaced with evoking sentiment. The underlying device of "making it personal" is also at the root of many ad hominem attacks, but this is not one of them. It is not to disparage opponents that getting personal here is for, but rather to inflame them.
Like all informal fallacies this one has a rational kernel to it. The point of real life arguments isn't academic, they are ultimately about how we should act and behave. And that depends not only on "cold reason", but also on value judgments of what is "best", and in case of crimes like rape and murder, on moral judgments of what is fair, just and right. Reason has limited application there, and evoking emotions is often a means to question our judgment and tune up our moral compass. This is why a justified response to a dismissive "this is no big deal" can be "you didn't live it", and why bringing up the horrors of slavery can be appropriate in debating white supremacy. There are times to be cold blooded, and there are times not to be, in good measure. What truly makes the OP example a fallacy is that it goes beyond that, and uses emotions to back something that is clearly over the top. An eye for an eye leaves the whole world blind.