Is empower considered an activated ability?

Yes. Empower is explicitly an Activated Ability keyword (Rule 827.1) — functionally short for "[Cost]: Empower this. Play only if not Empowered" (Rule 827.1.c.1).

So it follows the full activated ability process: you declare it in your Main Phase during an Open State, it goes on the Chain as a Pending item creating a Closed State, and opponents can respond with Reaction cards/abilities before it resolves (Rule 377.3).

One caveat: the Empowered status itself can also be granted by other effects (e.g., "Empower a unit"), which isn't an activated ability — only the keyword is (Rule 441, FAQ #11809).