In reply to Jørgen Boysen.

The quote is "For any distribution that satisfies certain conditions" [emphasis added] and the last sentence says "the Gumbel distribution can also model the maximum value for samples drawn from some non-normal distributions." So, no, Gumbel does not apply to all distributions.

The Gumbel distribution models the maximum of continuous distributions when (F(x))^n has an exponential decay (Type 1 distributions). For distributions with heavier tails (Type 2), you can use the Frechet distribution. For distributions with lighter tails (Type 3), you can use the Weibull distribution.