Lincoln died in 1865, but the oldest recordings are from the 1860s. The video is definitely a hoax (http://www.firstsounds.org/research/others/lincoln.php), but it's at least theoretically possible his voice could have been recorded. In fact I believe there are some even older recordings from the 1850s, but I don't think those have been successfully recovered yet.
These early recordings are incredibly crude, and they did not have the technology at the time to play them back. They were just experiments in trying to view sound waves, not attempts to preserve information for future generations.
