There are a variety of more-or-less sort-of correct answers below, but I'll throw in my two cents regardless. I am a nuclear physicist who spent a lot of time worrying about neutrons, which are a major source of backgrounds in neutrino detectors.

Two points made reply to you are correct: neutrons are radiation, but not electromagnetic radiation; and neutrons can make other things radioactive.

Some thing other people are saying are less correct: any individual neutron will deposit most of its energy in one place, but averaging over many neutrons their energy deposition will be spread out. Furthermore, neutrons will come out in all directions. The problem of neutron damage is not small, but no one seriously believes it's a show-stopper.

Neutrons are the exploding billiard-balls of nuclear physics. Fusion produces "fast" neutrons, with moderate energies. This is a deuterium-deuterium device, so most of the neutrons will come out with 2.4 MeV, which happens to be the same as fission neutrons. The DD reaction produces tritium as a byproduct about half the time, though, and DT fusion will lead to 14 MeV neutrons. There will be fewer of these in most designs, and some designs incorporate ideas to get rid of the tritium quickly to suppress these higher energy neutrons.

At high energies neutrons don't tend to interact very much with light nuclei, and for a variety of reasons fusion reactor design is dominated by light nuclei. What they do do is bounce off, which is where the billiard-ball analogy comes in. Each time a neutron bounces off another nucleus it loses energy (because the nucleus it bounces off of recoils, carrying some energy with it.) This is just pure Newtonian mechanics.

Neutrons typically travel a few metres in the process of slowing down, depending on the material. Light materials slow them down faster: a light ball bouncing off a heavy ball doesn't loss much energy, but bouncing off another light ball it does (hydrogen is the best material for slowing neutrons down because of this, and hydrogen-rich materials like water are good too.)

The neutron never completely stops because the nuclei it is bouncing off of are in thermal motion. At room temperature a neutron in thermal equilibrium moves at about 2200 m/s. But not for very long, because this is where the exploding comes in.

You can think of it in these terms: once thermalized, a neutron is passing by other nuclei rather slowly (2200 m/s is slow when you're a neutron). This gives it lots of time to react with nuclei, rather than just bouncing off, and eventually it does. When a nucleus absorbs a neutron it becomes a different isotope of the same element, and in many cases adding a neutron to a stable isotope makes it radioactive. Carbon-12 is a stable isotope that, with the addition of a neutron becomes carbon-13, and if it happens to get another neutron added later on, radioactive carbon-14.

Neutrons are a pain, even to fission engineers, and fission depends absolutely on them to happen. They get everywhere, are hard to shield, make stuff radioactive and damage materials. But we know pretty much how to deal with them, and it's unlikely they will make the difference between working and not working in a device like this.