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”.
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: