How did the Cenozoic animals go extinct?

The Holocene extinction includes the disappearance of large land animals known as megafauna, starting at the end of the last glacial period. Megafauna outside of the African mainland (thus excluding Madagascar), which did not evolve alongside humans, proved highly sensitive to the introduction of new predation, and many died out shortly after early humans began spreading and hunting across the Earth (many African species have also gone extinct in the Holocene, but – with few exceptions – megafauna of the mainland was largely unaffected until a few hundred years ago).

Big-game hunters. From the future. Time travel will be with us in the next 25 years or so, and Cenozoic tours will be very popular. Hope this helped.

Maybe they were hunted to extinction by early humans

I'm not sure what you're asking about.  We're currently in the Cenozoic.

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From the animals you mentioned, it appears you're talking about the Late (or 'Upper') Pleistocene Extinction, in which a lot of North American (and northern European) megafauna went extinct.  An event also referred to as the Younger Dryas.

Please note: the following explains just the Younger Dryas event, which is part of a larger series of events, known collectively as the Quaternary Extinctions.

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The current understanding goes like this:

1) The Laurentide Ice Sheet which had covered most of North America begins to melt as global temperatures recovered from the last Glacial Maximum.

2) As the melting begins, most of the meltwater flows down the Mississippi River Basin and into the Gulf of Mexico.

3) As the edge of the ice sheet retreats, a glacial lake forms behind an ice dam which traps a large amount of cold fresh water in the middle of the continent.  This glacial lake is known as Lake Agassiz.

4) Eventually, the ice dam collapses.  As the ice sheet has retreated farther north by this time, a huge amount of this cold fresh water is released down through the Great Lakes and the St. Lawrence River basin - into the north Atlantic.

5) This huge pulse of fresh water (less dense that the saltier seawater) disrupts the Atlantic Thermohaline circulation, preventing warm tropical water from leaving the equator, and refreezing everything that had just started to thaw.

Many key plant species in North America couldn't handle the abrupt change and died.  The food chain that depended on those plants crashed, and at the top of the chain the large herbivores and the large carnivores that fed on them went extinct.

Smaller animals adapted better, and survived.