I know China is a very big place but even so - 47,500 transactions per second would be almost quintiple what Visa handles across the entire world. With only 300 million users and primarily online usage (?) this claim feels a little suspect to me.

Given the wording "up to 2.85 million" I wonder if that is some freak spike caused by people's behaviour being synchronised externally (e.g. a fixed start time for the sale that people are waiting for). It's hard to imagine that they sustained anything close to that for the entire day.

So this is really a discussion about peak performance.

There's a discussion of such things here that might be useful:

It discusses various optimisations, like not actually sending tx data twice.

I wouldn't worry about it too much. It took decades for Visa to even approach 10,000 txns/sec. PayPal, I believe, still "only" handles a few hundred. And those services had the benefits of minimal competition, working in people's local currencies, integrated dispute mediation and not representing any real threat to the political status quo. Bitcoin isn't going to be needing to handle Alipay's level of traffic any time soon. 

Frankly, scaling is a nice problem to have, it means you're popular. It'd be a mistake to just blindly assume Bitcoin will take over the world. Growing market share is difficult. Worry more about how to get 300 million crazy users than the precise broadcast protocol that'd be needed to handle them ;)