Learn Dutch: Hij was de enige die boos was. - He was the only one who was angry.

When you turn an adjective into a noun to refer to a person, you use de. Here, de enige means "the only person" or "the only one" because it refers to Hij (he). The rule you learned about het applies to abstract ideas or things. "The only thing" would be het enige.

Since it translates to "who was angry," why don't we use wie instead of die?

English uses "who" for people and "that" for things, but Dutch usually uses die or dat for both when linking a clause back to a noun. Because de enige is a de-word, we use the relative pronoun die. You generally only use wie as a relative pronoun after a preposition (like de man met wie, "the man with whom").

Why is the second was at the very end of the sentence?

The part of the sentence die boos was is a subordinate clause. It doesn't stand on its own; it just adds information about de enige. In Dutch subordinate clauses, the verb is always pushed to the end.

If the sentence were "They were the only ones," would enige change?