The word "cuándo" is accented here because it is being used as an interrogative or exclamatory term, even though it appears in an indirect context rather than a direct question.

In your example:
"Yo ya sé cuándo salió esa película, fue en 2003."

The phrase "cuándo salió esa película" indirectly refers to a specific point in time when the movie came out. Even though the sentence is a statement, the clause retains its interrogative nature because it refers to the implied question of "when" the movie came out.

In Spanish, whenever "cuándo" is used to convey a question—whether direct or indirect—it requires an accent. If it were a non-interrogative usage (e.g., "cuando" meaning "when" in a time conjunction), it would not carry the accent.

For example:

Direct question: ¿Cuándo salió esa película?
Indirect question: Yo ya sé cuándo salió esa película.
Time conjunction (no accent): Cuando salió esa película, nadie fue a verla.
I hope this clears up the confusion! Feel free to ask if you have more questions.