JE is addressing a type of purely juridical universalism where God in effect says, “Okay, for your sins you will have to spend so many eons in jail” (i.e. like the merely legal interpretation of the last farthing warnings and parable in the Gospels) “and then after that I’ll take you to heaven, or give you a probationary period for repentance or something.” But the wicked are still being wicked during this period, so Edwards rightly asks: shouldn’t they be punished for that as well? Or not? If not, then they might as well not have been punished in the first place! If so, then in fact there would be a rolling never-ending wave of judgments against the wicked for which they would have to be punished, which means they will never be getting out of torment.
This is why Edwards states that the idea overthrows itself. He is, however, here addressing a notion of universalism where the proponent admits that the punishment for sin must be so long as to seem (by contrast with our brief span of life before judgment) everlasting, with no mitigation for repentance. JE’s answer to this is that it is not rational to suppose that God would continue the punishments once true repentance has been achieved, therefore if the punishments (as these proponents allow) must be continuing, then it must be because the sinners are impenitent. But if they are impenitent, then they are only continuing to build up for themselves in exponential waves longer and longer terms of sentence; like someone sent to jail for murder who then continues murdering while in jail, constantly adding onto his sentence.
Please note that this is only one page of JE’s chapter against non-eternal torment in this book; his whole argument against universalism shouldn’t be regarded as this one page. (He tends to go back and forth between topics in this chapter; for example, paragraph 22 is also about God loving those whom He is punishing in Gehenna and seeking their salvation.)