NOTE: this has been confirmed by Apple as intended behavior. Sometimes, what is backed by HTML is not meant to present itself as a webpage. Therefore, VoiceOver sees HTML content but is not supposed to navigate it like a webpage, thus arrow keys will not work as they would in webpages. This bug has been marked as fixed due to this new information.
Some HTML areas can be read with the arrow keys, but some cannot. For instance, the App Store's HTML content does not respond to arrow keys at all.