Learn Spanish (Latin America): ¡Qué coraje que no usen la instalación! - How infuriating that they are not using the facility!

Because the sentence starts with an emotional exclamation: ¡Qué coraje que...! (How infuriating that...). Whenever you use ¡Qué + noun or adjective + que to express a reaction, judgment, or feeling about a situation, the verb in the following clause must be in the subjunctive.

I thought coraje meant courage. Why does it mean infuriating here?

While it does mean courage, in many parts of Latin America (especially Mexico), coraje is also very commonly used to mean anger, rage, or frustration. So, saying ¡Qué coraje! is a natural way to say "How infuriating!" or "What a pain!" rather than talking about bravery.

Why are there two types of que in this sentence?

They serve two different roles. The first one is qué with an accent mark, which acts as the exclamatory "what" or "how" (¡Qué coraje! = What anger!). The second one is que without an accent, which acts as the connecting word "that" (que no usen... = that they don't use...).

Who is the subject of usen in this sentence?

Since usen is the third-person plural form, the dropped subject is "they" (ellos or ellas) or the formal plural "you" (ustedes). The English translation assumes "they" based on typical context, but it could easily mean "How infuriating that you all are not using the facility!"