From what I gather, the Bitcoin mining is really just a way to incentivize device and chip makers to include 21's tech, in the short term.

I can think of two longer term benefits that only kick in once they actually get their tech widely distributed:

1) A low-power hardware wallet in your smartphone, smartwatch, etc, allowing people to make Bitcoin transactions from anywhere to anyone without needing to go through a middleman. Finally, true digital cash.

2) A Bitcoin private key on every Internet of Things device, which means that you'll be able to use some sort of fancy multisig side-chain algorithm (I'm no expert here) to verify ownership of all of your "stuff." This will disincentivize theft in a big way.

It's worth noting that, to make mining a viable way to bootstrap this whole thing, they need to be at the cutting edge of Bitcoin ASIC tech for multiple iterations of Moore's Law. Which is probably why they raised so much money.