Before we get to the issue of the Pleistocene re-wilding of North America, some may be wondering "just what exactly does "Pleistocene" mean?
"Pleistocene" refers to a specific interval of geologic time that is estimated to have lasted from 1.8 million years ago to 10 thousand years ago. It is best remembered as being the time of the last major Ice Age. Many scientists believe that "today's" warm climate is simply a natural rebound (or recovery) from the last Ice Age.
Referring to the accepted Geologic Time Scale (different versions may have slightly different age estimates), geologic time is divided into a hierarchy of time periods, based on different criteria. Most of the time boundaries are based on significant changes in the sedimentary rock and fossil record, as observed in 18th and 19th century Europe, where most of the present Geologic Time Scale was devised and defined. All of the time units, within the various categories, are of differing lengths.
The broadest time periods (at the top of the hierarchy) are "Eons", which cover hundreds of millions of years. We live in the Phanerozoic Eon, which began approximately 544 million years ago with the first widespread appearance of hard-shelled marine organisms.
Eons are divided into "Eras", which cover tens of millions of years. We live in the Cenozoic Era, which began approximately 66 million years ago with the end of the Mesozoic Era, when the dinosaurs became extinct.
Eras are divided into "Periods", which cover millions to tens of millions of years. The Cenozoic Era consists of the Tertiary Period (66 million years ago to 1.8 million years ago) and the Quaternary Period (1.8 million years ago to the present).
Periods are divided into "Epochs", which cover hundreds of thousands of years to millions of years. The Quaternary Period consists of the Pleistocene Epoch (1.8 million to 10 thousand years ago) and the Holocene (or Recent) Epoch (10 thousand years ago to present). The dividing "line" between the two epochs is the last major ice age.
As details of the geologic record become less distinct as we go back in time, the Epoch time classification is only used on a world-wide basis for the Cenozoic Era, i.e., the last 66 million years.
With the mass extinction at the end of the Mesozoic Era (and the end of the Cretaceous Period, too), approximately 66 million years ago, the niches and habitats of the world's ecosystems were "emptied out" of dinosaurs and other organisms. The mammal and bird survivors refilled these vacant niches and habitats with an "Adaptive Radiation", i.e., whereas the previous Mesozoic Era is known as the "Age of Reptiles", the Cenozoic Era is known as the "Age of Mammals".
With the natural global warming that ended the last Ice Age, human populations rapidly grew, cultures developed and humans migrated, in our case, most notably from Asia into North America. There was a significant extinction of large Pleistocene mammals in North America, attributed to human activities by some scientists, while others consider other possible causes (but not excluding the "human effect").
The article linked at the top of this post addresses the plans to introduce large African and Asian mammals (megafauna) to North America, to "replace" that which was lost in the last 10,000 years or so.