In terms of overall number of mammal species there perhaps aren't that many fewer than were present in the Pleistocene.
As a megafauna enthusiast though, I agree that most of the coolest mammal species were taken out by European settlers 300 years ago (brown bears, mountain lions, wolves) and by the first American settlers 10,000 years before that (mammoths, smilodons, camels, etc.).
It says this about museum specimens: "Skeletal and skin specimens were not collected by zoologists (Sealfon 2007). Sea Mink remains, primarily cranial, have been excavated from Native American shell middens, although no collector is known to have preserved a complete specimen (Dunstone 1993). Specimens can be found in the collections of the American Museum of Natural History, New York (AMNH); the Frick Collection of the American Museum of Natural History, New York (F:AM); and the Maine State Museum, Augusta (MSM). (Sealfon 2007)"
Is that 73% statistic referring to all mammals, or mammals over a certain body size? Have any bats and rodents gone extinct in the US? I would think that they would account for the bulk of North American mammal diversity, but that may be at the species rather than genera level.