From the wikipedia article, we see that:
IRLS is used to find the maximum likelihood estimates of a generalized linear model, ...
However, they describe the algorithm as an iterated algorithm that minimises objective functions of the following form:
$$\underset{\boldsymbol\beta} {\operatorname{arg\,min}} \sum_{i=1}^n \big| y_i - f_i (\boldsymbol\beta) \big|^p$$
This does not look like a minimiser for the log-likelihood $\ell(\mathbf{y}|\theta)$.
