Yeah, that's what Chrome's "install" thing does.
As opposed to run it in...? As a native binary? Chrome doesn't do that, it merely has Flash built-in right off the bat without manually installing the extension.

What an odd game

No, it doesn't utilize Flash. The Chrome version runs in HTML5. The game actually switches to the inferior Flash version if your browser doesn't support the web technologies behind the Chrome version of the game.

IE9 and Firefox 4 and better support HTML5... Its not like Chrome nas a unique HTML5 features. lol

Funny then, how the error page in 64-bit IE9 says "Install Google Chrome, [...] that comes with Flash built-in." On the other hand, on closer inspection it seems you're right, I don't get the normal flash pop-up menu in any browser, nor does the source indicate flash anywhere.

Firefox 4 and Chrome gets the game served through <canvas>.
Safari 5 gets a buttload of created/removed/modified divs.
Opera 11 gets the same as Safari, except it doesn't go beyond the loading screen.
IE9 64-bit gets an error about Flash not being present.
IE9 32-bit gets the same as Safari.
IE10 Platform Preview gets to the loading screen but doesn't actually show an image.

This leads me to believe Flash is being used in some form (for the non-canvas version at least), though not for the whole game.

The version in Chrome better not be using Flash, considering their whole deal at I/O about it was about how it didn't use it, heh. The Rovio rep indicated that other technologies would be used to be sure that all browsers would be compatible, but that the version for Chrome was going to use the fullest of Chrome's developer API's and whatnot to provide the "best experience" in Chrome.

It doesn't like Chromium on my netbook (complains about Flash not being installed), so now I'm fairly sure it uses Flash in some form (however small) for all browsers.