I don't think there's a way to get to that context menu (or for that matter do pretty much anything else) in the modern/metro/tiled version of Skype, otherwise it would be described in the Skype Win8 FAQ page. (Notice that the equivalent Desktop FAQ page does describe the edit button.)
It looks like the modern/metro/tiled Skype version needs a lot of work. Which is sort of sad, considering that it's basically Microsoft's canonical Windows 8 instant messaging app. But I digress.
We’re working hard on bringing all of our features to Skype for Windows 8, but if you need to make group video calls, send files or share screens, you can still do so with Skype for Windows desktop.
(Source)