The quote that is supposed to contain a "snuck premise" is the following (about 6:20-6:29):
As you may have noticed I'm mostly against abortion. If you want to go to Planned Parenthood to get a contraceptive, go for it. I don't care. I do care when you start killing babies."
The "killing babies" is referred to as the "snuck premise", an introduction of the point of contention as a given.
This may be seen as a kind of red herring. I imagine he redirected the focus of the argument from something else to the phrase "killing babies".
Here are some synonyms for red herring on the Logically Fallacious site:
beside the point, misdirection [form of], changing the subject, false emphasis, the Chewbacca defense, irrelevant conclusion, irrelevant thesis, clouding the issue, ignorance of refutation
This might work as a description of this rhetorical technique if his opponents felt distracted by having to defend against his claim of "killing babies".
However, it is also possible that they were discussing abortion and he was just reiterating his position as a given. That would also be a rhetorical technique perhaps related to "argument by repetition".
Charisma on Command channel, "7 Reasons Ben Shapiro Is So Dominant in Debates" https://youtu.be/JY5t6iUzajk?t=381
"Argument by Repetition" Logically Fallacious https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/49/Argument-by-Repetition
"Red Herring" Logically Fallacious https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/150/Red-Herring