I'm curious about their approach.
Very high TX/seconds can be achieved easily but it introduces problems such as rapid blockchain bloat (the size of the blockchain grows rapidly to gigabytes or even terrabytes of data) or too short block times that can cause forks or very high block sizes which require tons of bandwidth excluding regular users to be full nodes.
Even if each transaction would only be 100 bytes each (Bitcoin has about ~3 times bigger transaction sizes on average), each block would use ~42 MB of disk space. That's 42 MB per second. Even one hundredth of that would require a continous bandwidth of 429 KB/s. And it likely wouldn't be perfectly continuous at all so you would need massive speed spikes not to lag behind the network.
And that amount of transaction surely requires a lot of CPU power to actually process.
They talk about account balances being verifiable without requiring the entire ledger...though they don't detail how anywhere.
I would assume that it's doing something like Open Transactions, where each transaction includes the previous balance and the amount. From that you can determine the current balance, and therefore run heavy pruning.