How do I play the full version of Plants vs Zombies under Chrome OS on a Chromebox?

I have a Samsung Chromebox running Google Chrome OS. I've been playing the trial version of Plants vs Zombies online at http://chrome.plantsvszombies.com/, and loving it.

I've tried to purchase a full copy of the game, and am automatically directed to the 'PC' download. This is an .exe file, which Chrome OS doesn't know how to run. I don't see any way to select my hardware/software profile from the menus, or any way to apply my registration number within the trial version. On the other hand, there is nothing anywhere to indicate that upgrading the game is not possible.

Can the full version of Plants vs Zombies be played on Google Chrome OS? If so, how?

The Chrome Web store and the PopCap website both indicate that the browser based version of Plants vs Zombies is a free trial, but neither give any indication of a browser based 'full version'.

The Chrome Web store indicates that the "full version" of the game is specifically for Windows and Mac.

You can install Bluestacks, an Android emulator. Then install Plants vs. Zombies FREE from the Google Play Store.