Learn French: Que le traître se taise immédiatement ! - Let the traitor keep quiet immediately!

Starting a sentence with Que followed by the subjunctive is how you give a third-person command in French. Since you cannot use the normal imperative (command) form for someone who isn't you, we, or you-all, you use this structure to mean "Let him..." or "He must...".

What is the infinitive of the verb se taise and why is it conjugated like this here?

The infinitive is the reflexive verb se taire (to be quiet or to keep quiet). It is conjugated in the present subjunctive because the third-person command structure (Que + subject + verb) always requires the subjunctive mood.

How is this different from just saying Le traître doit se taire immédiatement?

Saying doit se taire simply states an obligation, like "The traitor has to keep quiet." Using Que le traître se taise is a direct, authoritative command or decree thrown into the room, making it much stronger and more urgent.

Does this kind of command sound highly formal or theatrical?

The grammatical structure itself is actually very common in everyday spoken French (for example, Qu'il parte ! for "Let him leave!"). However, pairing this authoritative command structure with a dramatic word like le traître (the traitor) gives this specific sentence a very theatrical or literary feel.