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.