I've come to realize this is genius for two reasons:
1. Amazon is pitting governments against each other. This sort of thing is a well-known and well-trodden path so it's nothing new but the real genius part is:
2. Once Amazon has two headquarters they're no longer at the mercy of the city of Seattle and the state of Washington.
Let me elaborate: take Google, which is heavily invested in Mountain View. Essentially the Mountain View City Council has them where they want them. Google wants to stay in MTV (and, more importantly, expand in MTV) so whatever taxes and conditions the council wants to put on them, well they kind of have to suck it up.
The latest of these is MTV forbidding free food in new campuses because it hurts local business.
Now Google has obviously expanded well beyond MTV at this point (Redwood City, San Antonio Boulevard, Sunnyvale, San Jose, San Francisco). But these are less than ideal solutions. Move a team from MTV to Sunnyvale and you've added 10-20 minutes to the commute of everyone living in SF. Getting around "campus" requires a transit system all of its own.
Compare this to Amazon's future position: if Seattle decides to put an onerous (from Amazon's position) tax or set of conditions on them they can simply say "we'll expand our other campus instead". So they're not beholden to one town or city like the SV giants are (specifically Mountain View, Cupertino and Menlo Park).
I really wish the SV giants would take this approach.
Also, as others have mentioned, the cost of living for those not fortunate enough to be in tech is horrendous in SV. You can blame small-minded NIMBYist towns and voters for this if you like but (IMHO) that's shortsighted. By continuing to exist there and expand there the giants are supporting those anti-progressive positions.
At some point you're either part of the solution or part of the problem and (IMHO) continuing to expand in SV makes you part of the problem.