I assume the chromebooks support html5 video, which youtube also supports. Apple was able to have iPhones still work with youtube without supporting flash, so Google could have found a similar workaround even without including html5 video tags.

Though the iPhone uses a YouTube app, which isn't the web. The allure of the Chromebook is that it can play the whole web, and YouTube is a big part of that. YouTube does have html5 video, but it is still in beta and isn't available for all videos. And it is opt-in.

In addition, with the focus on enterprise and education, I believe that Chromebooks had to support flash as a requirement.