I am not at all sure why Ted Kaczynski made this gun, unless it was to avoid the detection of having to buy one. It's remarkable in its craftsmanship. Don't know if it worked, but given how meticulous he was, it probably did. This photo is part of the government evidence against him, found at this CBS site, without much explanation. If you know more, write.
In the comments, Cory H. supplied the answer to why the Unabomber made this gun, and whether it works:
Reprinted from his diary in the Government's Sentencing Memorandum, which explains that agents discovered a completely homemade, operable handgun, as well as a corresponding written description of its creation and purpose:
[A] few days ago I finished making a twenty two caliber pistol. This took me a long time, for a year and a half, thereby preventing me from working on some other projects I would have liked to carry out. Gun works well and I get as much accuracy out of it as I'd expect for an inexperienced pistol shot like me. It is equipped with improvised silencer which does not work as well as I hoped. At a guess it cuts noise down to maybe one third. It is said that it is easy for machinist to make a gun, but of course I did not have machine tools, but only a few files, hacksaw blades, small vice, a rickety hand drill, etc. I took the barrel from an old pneumatic pistol. I made the other parts out of several metal pieces. Most of them come from the old abandoned cars near here. I needed to make the parts with enough precision but I made them well and I'm very satisfied. I want to use the gun as a homicide weapon.
From Ex. 91