Will Irencrag Pyromancer's ability trigger when it's killed by Ob Nixilis, the Hate-Twisted?

You perform instructions in an ability in the order in which they are written. So, in this scenario, the creature is destroyed then you draw the cards. Creatures that are destroyed die immediately, so the Pyromancer is already dead by the time you draw the cards and its triggered ability will not trigger.

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Rules section 608 describes how to resolve spells and abilities, and rule 608.2c says

The controller of the spell or ability follows its instructions in the order written. However, replacement effects may modify these actions. In some cases, later text on the card may modify the meaning of earlier text (for example, “Destroy target creature. It can’t be regenerated” or “Counter target spell. If that spell is countered this way, put it on top of its owner’s library instead of into its owner’s graveyard.”) Don’t just apply effects step by step without thinking in these cases—read the whole text and apply the rules of English to the text.