Learn Dutch: Hij weigert de nota te archiveren omdat de stempel ontbreekt. - He refuses to archive the bill because the stamp is missing.

No, here it is a standard te + infinitive phrase acting as the object of the verb weigeren (to refuse). If we wanted to use the attributive modal infinitive being taught in this lesson, we would turn it into an adjective placed directly before the noun: de te archiveren nota (the bill to be archived).

Why is 'is missing' translated as just one word, ontbreekt?

In English, 'is missing' uses the verb 'to be' plus a participle. In Dutch, ontbreken is a standalone verb that inherently means 'to be missing' or 'to lack'. You don't need to add a translation for 'is', as the single verb does all the work.

Just a refresher: why does ontbreekt go at the very end of the sentence?

Because the clause is introduced by omdat (because), which is a subordinating conjunction. In Dutch, subordinating conjunctions always push the conjugated verb to the end of their specific clause.

I've seen het stempel before. Is de stempel also correct?

Yes, both are correct! Stempel is one of the few Dutch nouns that can take either de or het. In everyday practice, Dutch speakers tend to use de stempel for the physical tool or ink mark, and het stempel for figurative contexts, but you won't be misunderstood using either.