They overlapped with humans (and dogs), and didn't go quite extinct until sometime after 7000BC (maybe 6000). The explanations I've seen most frequently (probably they borrow from each other) are that when the big animals died out the wolves and smaller canids out-competed them, and that some disease knocked them down.
The first might kind of work if they were slower than wolves, and the wolves caught more deer and rabbits and whatnot. I'm guessing that a faceoff of a wolf pack and dire wolf pack over an elk carcass might favor the dire wolves, but most kills were probably smaller.
The second--that dogs brought disease and the dire wolves couldn't mate with dogs (like wolves and coyotes can) to pick up disease resistance--doesn't seem to have very plausible timing. Or obvious significant fractions of dog admixtures in wolves. Maybe a disease just hit them harder, and wolves took over their niches and out-bred them.
I wonder what would have happened if dire wolves had no fear of humans. People take personal predators kind of seriously. Attacking a pack might not turn out well, but wiping out dens might be feasible.
I don't know of any Amer-Indian legends about them. Since they were so close in size to grey wolves, there might not been enough distinctive about them to merit a separate category. Or the modern Amer-Indians may have come later, after most of the dire wolves were gone. Or they just didn't keep stories that long--after all, many tribes deny they came from elsewhere.