This is a dark game. It includes elements of radiation, progressive biohazards, existential dread, and potentially, eventual death. It is quite direct and minimal in the depictions of hazards in general. It would be… jank to insert confusing new names for something there’s already a very easily understood shorthand for. So there’s that.
At the same time… Dr. Kel’s symptoms are in actual fact much more consistent with (comically rapid) acute radiation exposure syndrome or even radiation burns, which tend to be the things that kill you at short timescales. It would be rather nice if we could call it that. If he’s taking any medications, they are things like potassium iodide and chelating agents, but most games hand-wave over the details of how radioactive contamination actually works.
For examples of how this is approached with at least diegetic effectiveness: see the Fallout series.
Cancer is the thing you get later if you survive all that, but Dr. Kel is not at the base long enough for such to develop. Unless it’s some kind of weird violently accelerated alien cancer. Then you might as well call it Bao disease for all the help that man will give you, I guess.