It's listed there under False cognates.
> evidence indicates arigatō has a purely Japanese origin
I remain suspicious, though. Maybe what happened was the popularization of an existing Japanese term under the influence of Portuguese Jesuits, since it sounded similar to obrigado?
Perfectly possible. I think I've seen evidence elsewhere of similar but unrelated words influencing each other. For example, round about where I live the Romany word "shan" is used meaning "mean" or "worthless", but it seems to have been influenced by the unrelated "sean" in Gaelic (also pronounced "shan") which means "old". So it's come to mean something worn out as well.
In general, I think this phenomenon is called "phono-semantic matching": https://en.wikipedia.org/wiki/Phono-semantic_matching.