Yeah this quote doesn't really work if the metric is your actual goal. If I make daily revenue for my e-commerce company (or daily ad engagement for Meta) my goal, it does not cease to be useful.

By making the metric the goal, it could be that the underlying assumptions change. Maybe previously all time spent on Facebook was "positive" time where the user feels engaged and is interested in ads. After adding dumb notifications. The time spent might become partially "positive" and partially "negative", where the user feels abused and might hate the ads. Is the metric still the goal then?