I looked into this, and Ft. Collins is a "Home Rule Municipality" under state law, meaning it can name itself either a town or city. It seems to have chosen to be a city, so you're right.
Around the world, it seems that there's one consistent criterion for something being a city: it must have self-rule and a certain amount of government structure. Some places (notably not the US) have population requirements, but those tend to be really low (100-1,000 people)[1].
I personally appreciate the headline saying "town" in a colloquial sense, because I don't think of 170,000 as "huge" and it's significant that it's not a large city doing this.
For context, Ft. Collins is not in the top 150 most populous US cities, and to even reach the top 50, it would have to more than double in size.
1. https://www.thoughtco.com/difference-between-a-city-and-a-to...