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Yes, it seems the warthog just has the usual forward-back and left-right movements as it is closely based on the aircraft stick.
The z-axis on a joystick is where you twist the stick instead of pushing/pulling it.
Do you need it? Well, it's not absolutely necessary, but can be useful - it's another axis after all.
In the context of ED, I think most would use it for yaw as that puts all the rotational controls on the stick, but it comes down to what you are comfortable with and how you fly. While most ships in ED have weak/slow yaw, you do still need to have it somewhere in your controls to give you maximum control over your ship. So if you don't have it as a twist axis on the stick you'll need to set it up somewhere else on a control that could have been used for something else. That would probably apply to other space sims as well.
For aircraft sims, on the other hand, you'd be more likely to get/use pedals for the yaw axis (as that's how planes work), so wouldn't need twist. Of course, even if you have a stick with twist, you don't need to configure it if you are playing a flight sim.
