Also in Chinese, reciting the times tables are shorter and (unproven) probably easier to memorise, "3 1 3, 3 2 6, 3 3 9". Although I'm not sure why that can't be done in English either.
It was a long time ago for me now, but I learned the times tables (using your example) as "three ones'r three, three twos'r six, three three's'r nine" etc. Seems like it's just the addition of a single "zrr" syllable after both numbers to me, and to me that seems easier to say than e.g. "3 2 6", maybe just because it's an automatic reflex to add the extra sound and not adding it makes it seem just a stream of numbers out of context.
Quickness is definitely not prioritized.
I've never been to China, and have no idea if this is wide-spread — I saw a documentary on children in China being taught mathematics at an early age using an abacus. Eventually, they remove the abacus but the child still mimes using it. And then gradually this disappears too.
Essentially they're training their muscle-memory to do their maths for them.
It was quite extraordinary to see, especially since I, while I flatter myself I'm reasonably intelligent in some areas, and worked in programming and related areas for many years, my ability to do any maths without a pencil and paper is abysmal. OTOH, it's not impossible I have un-diagnosed dyscalculia.
And, as it turns out, they measured something else indeed. They measured recall of a visual scene after guiding subjects in different ways. English speakers were guided with e.g. clock and clown or clock and mirror. The first pair have some overlap, so (as theory suggests) subjects start looking at both. The second pair has no overlap, so the word clock doesn't make the subject scan for the mirror. Then they tested recall on these pictures. There are differences between people with different language proficiency, but they are small.
So it doesn't show that speakers of different languages remember visual scenes differently, but rather that people only recognize objects from partially heard words quickly in the language(s) they're proficient in.
I wish they'd stop clickbaiting for this kind of technical studies.