Animals come from a single fertilized egg that divides into multiple living cells that organize themselves as directed by DNA to form complex bodies to do biological functions, including the means to obtain food, digest food, obtain and distribute oxygen, use the food and oxygen to power functions, and get rid of waste. They produce sperm and egg cells to reproduce. They experience mutations. They grow to adults through many stages, each viable, and each formed by controlling when certain genes activate. They do this using carbon based organic molecules.
Your watch is a non- living machine that does none of this.
If you show me something that does all this, I would call it an animal.