Definition 1:
A smoothie (also known as a "smoothy") is a blended, chilled, sometimes sweetened beverage made from fresh fruit (fruit smoothie) or vegetables and in special cases can contain chocolate.
Definition 2:
[...] a thick beverage of fruit pureed in a blender with ice and milk, yogurt, or juice.
- Ketchup is not considered a beverage by anybody I know.
- Ketchup is not made only from fresh fruit and ice/milk/yogurt/juice. It has many other ingredients.
- Ketchup is probably not made in a blender.
- There are plenty of food items made from fruit that aren't smoothies (is applesauce a "smoothie?").
So, no, it's not a smoothie simply because it contains a fruit.