Language is not essential for the cognitive processes that underlie thought

Is this the death of the Sapir-Whorf theory?

Sapir-Whorf is not alive.

No. Just because words are not needed for cognitive processes, does not mean that people still can and do think in language. The properties of that language could then influence thought. This is known as the Weak Sapir-Whorf hypothesis (note "hypothesis", not "theory").

Yep, this pretty accurately describes the way of think. I have a pretty heavy inner monologue, but it's not the only way I think. I've found that words are the way I "organize" my thoughts from muddled general ideas mixed with feelings into concise ideas that I can understand and gain insights from. I often won't fully grasp the significance of an idea I have until I talk it out with someone and find a way to put it into words that distill whatever I'm thinking into a more minimal form.

Somewhat relatedly, I've started suspecting over the past few years that this is why I struggle to multitask or split my attention; while I can ruminate on several things at once, the "output" of my thinking is bottlenecked by a single stream that requires me to focus on exclusively to get a anything useful from it. Realizing this has actually helped me quite a bit in terms of being more productive because I can avoid setting myself up for failure by trying to get too much done at once and failing rather than tackling things one at a time.

It was dead before.

This also doesn't say that the non-literal cognitive process is DNA-wired logic. Could very well be culturally constructed as well.

IMO this rather reinforce Sapir-Whorf positions than refute, it means more than literal language/grammar influence thoughts. That's directly against UG theory that predetermined rigid grammar is all you need.