I think I've figured it out (just tried again on Orion 0.99.109 and am seeing the same behavior):
If I'm browsing in Horizontal Tabs mode, right-clicking any tab does not show a context menu. But, it depends on how I right-click. If I hold the Control key and tap my trackpad with one finger, nothing happens. If I tap my trackpad with two fingers (without holding Control), I get the context menu. So when in Horizontal Tabs mode, Control+right-click doesn't work at all (on both pinned and non-pinned tabs).
In Vertical Tabs mode, the behavior is slightly different: I can both Control+right-click and two-finger-tap a non-pinned-tab, but I can only two-finger-tap a pinned tab to get the context menu to show up.
Hope that makes sense.