Passenger Pigeons. Dodos. Both made extinct via predation. The fact that it was hman predation shouldn't matter much, but if you really want to only consider non-humans then rats and cats and pigs have made dozens of species extinct.

https://www.pnas.org/doi/10.1073/pnas.1602480113

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You could make a good argument that aurochs went extinct due to "predatjon" before the modern era. Humans and other large predators like wolves heavily depended on them for food, and as the climate changed and predator populations boomed, macrofauna couldn't reproduce fast enough to survive. Humans got ahead of the crisis by domesticating oxen right as the last herds disappeared

It's really hard to categorize "why" and "how" a species went extinct if we don't have direct observation, so we really only have that kind of understanding of much more modern extinctions. Even for the dinosaurs, we know a) a space rock of some kind hit. B) the climate changed drastically overnight, and we can measure the effect on plants and the atmosphere. And c) the dinosaurs mostly died off. While we can theorize and use good techniques to analyze the evidence we have, we simply cannot know if the last brontosaurus was eaten to death or starved

Those three species alone are responsible for like half the extinctions in the last 400 years

I suspect it's effectively impossible to produce the kind of answer you are looking for. In order to make a determination that a species went extinct solely due to predation, we would need to have observed it very closely, which effectively excludes your qualifier "free of human interference." Also, you can't really attribute extinction solely to any one factor, unless you mean, "was the last individual killed by as predator, in its natural environment without human interaction of any kind?", or some other really specifically qualified question.

I guarantee that many species have gone extinct in large part due to pressure from predation. The Lotka–Volterra equations describe an idealized predator-prey dynamic where the populations have a stable oscillation without a possibility of extinction. In reality, many predation dynamics come so close to prey extinction that small fluctuations at the right time can reduce the prey population below a viable size.

Keep in mind, that natural selection can only act on existing variation in a population, so a prey species likely won't even have the ability to respond in a meaningful way to a significant predatory adaptations. This will normally just alter the dynamic and result in more extreme oscillations, but not necessarily result in extinction.

Couldn’t one argue those species were propagated by humans as well?

Precisely- we have really good models for "natural" dynamics like predator introduction that should result in extinctions from predation pressure. And there are lots of examples of that happening due to direct human interference or climate change. But it's probably not broadly possible to produce an example like what OP might be looking for, since any extinctions observed by modern science are influenced by human activities at every level

even when predation is the major effect, some individuals of a species will always also die because of a range of other causes. infections and other diseases, injury, limited food, dehydration, frost, natural disasters, etc

but yes, excess predation can make a species at risk of extinction