There seems to be no way to control the volume of individual Metro apps from a single interface, which certainly seems like a step back to me.
All you can do (in most cases) is select Settings from the Charms bar (Win+I) and click the speaker icon, or use the desktop volume control from the tray/notification area.
However, if an app does provide its own volume control you should be able to locate it by looking under its own Settings in the Charms bar.
Edit: Apparently, not only is the lack of a Metro audio mixer by design, Microsoft is also discouraging devs from including per-app volume controls as per this MSDN blog post:
There is no audio mixer in this environment as there is in the desktop. It still exists for desktop applications, but your app won’t show up here because we felt it was not a great experience to pop out into desktop to adjust relative app volumes. Instead, we are encouraging apps to not include volume controls. This way users are focused on the master volume control which helps simplify the entire volume experience as well – but that’s a different story.
(Note: Substitute "simplify" with "dumb down").
Edit 2: While a third-party volume mixer called EarTrumpet has enabled this functionality on Windows 10 since July 2015, it has shamefully taken Microsoft nearly 5 years to finally add Metro/Modern/UWP app support to Windows' own volume mixer in the Windows 10 Insider Preview Build 16193:
We’ve updated the Volume Mixer to now include UWP apps (like Microsoft Edge, or Groove Music), so you can set their volume without impacting the overall system volume. ... Note: UWP apps will only appear in the Volume Mixer once they start playing sound. To open the Volume Mixer, right-click on the speaker icon in the taskbar.