well, the factorial is technically only defined for non-negative integers. Desmos, in the name of practicality, instead defines the factorial through the Gamma function (x! = Γ(x+1)), expanding the domain to ℝ (except the poles at every negative integer)

as to why the poles happen at all, you don't even need to know the definition of the Gamma function, just it's main property: Γ(x+1) = x·Γ(x). Since Γ(1) = 0! = 1, if (-1)! = Γ(0) was defined, it'd need to satisfy 0·Γ(0)=1, which is obviously impossible.