Here's how their typical financial offer is structured for new software engineers:
1st year: signing bonus + relocation bonus + 5% of stock grant
2nd year: signing bonus + 15% stock grant
3rd year: 40% stock grant
4th year: 40% stock grant
If you quit within the first year, you have to give the relocation and signing bonus back. That's much much more than $1k. So there's a strong financial incentive / golden handcuffs to keep you there for at least 1-2 years, even if you are unhappy!
After the 2nd year, the financial incentive of staying is still there in form of the large stock grant (which has grown due to their stock price rising) that you've been promised and waiting on for a long time.
I can see someone rationally and happily taking the incentive after the third or fourth years and quit (i.e. after they've done damage to the work environment as an unhappy/unmotivated employee, and no longer have to give a fortune back to the company)... but before then, I doubt it'll change the behavior of any currently employed, overworked, over-paged, under-paid, under-appreciated software engineers.
Who this policy might affect though is future hires, and their perception of Amazon. People who have a choice between offers from MS and Amazon for example. They might consider this an interesting policy and assume that it would have improved employee morale at Amazon even though it's common knowledge that Amazon has terrible work life balance, etc.
I should also note that the Zappos policy makes a lot of sense to me, but this is very different from that, as is the employee culture of Zappos from Amazon.