Random ≠ arbitrary
Sure, though if you're looking to be pedantic, the keys they're asking you to press are neither random nor arbitrary
Edit: perhaps you're making the case that the user doesn't choose which key. This is true—but the important point is that one of the two parties did choose the specific key to press.
Edit2: For those downvoting, perhaps you could articulate why.
The American Heritage® Dictionary of the English Language, 5th Edition defines arbitrary as
> Determined by chance, whim, or impulse, and not by necessity, reason, or principle.
But the choices seem to be based on reason or principle.
that definitely does not sound arbitrary to me.