What context needs to be ignored? Ketchup is a sauce, which when added to completed food becomes a condiment, just like all sauces. Plenty of dishes are cooked with ketchup in the cooking process. The conclusion from the article you posted:
when it comes to the question of condiment or sauce, the answer is “both”.
Obviously it’s a sauce. I looked up the definition to try and figure out why they would say it isn’t, and I still don’t see it.
“a liquid or semisolid food mixture used especially as a topping or ingredient for adding to or enhancing the flavor of a dish”
There’s a lot more nuance in the definition in a culinary context: https://www.mashed.com/1338901/difference-between-sauce-condiment-dip/
But ignoring that context, yes, ketchup meets the literal definition of a sauce.
What context needs to be ignored? Ketchup is a sauce, which when added to completed food becomes a condiment, just like all sauces. Plenty of dishes are cooked with ketchup in the cooking process. The conclusion from the article you posted: