I guess the real mistake in the game is that there actually are buffalos/bisons.
Red dead redemption is set in the year 1911, and at that time there was pretty much not a single bison left in the USA. Within just a few decades in the 19th century, dozens of million bisons were killed, and by 1902 there were only 23 left in whole north America. A guy called George Bird Grinnell saved the species by taking them to a safe area - if it hadn't been for this guy, the bison would have been distinct by 1911.
Those are all bison heads:








