Is the %V/V composition defined for homogeneous mixtures?
Let's be clear on what percent by volume means.  If I say component $X$ is 25% by volume of a mixture of $X$ and $Y$, with a total volume of 1 L, it does not mean there is some 250 mL portion of the mixture that is solely occupied by $X$.  That wouldn't be a mixture.  It doesn't even mean that if I mentally subdivide that 1 L mixture into tiny identical cubes, one for each atom or molecule, then 1/4 of those cubes are occupied by atoms or molecules of $X$.

Instead, all it means is that I can prepare 1 L of the mixture by mixing some volume $V_X$ of $X$ and 3 times that volume ($V_Y = 3 V_X$) of Y.  There's not even any guarantee that $V_X = \pu{250 mL}$, since sometimes volumes are non-additive, that is, $V_X + V_Y \neq \pu{1 L}$.

Now as it happens, for ideal gases, which the atmosphere is close to being, you can mentally subdivide the volume into tiny little equal-sized cubes, one for each atom or molecule in the mixture, and on average there would be one atom/molecule of $X$ in each fourth cube if $X$ is 25% by volume of the mixture.  (I emphasize "on average" because of course since the gas atoms or molecules are continuously moving around randomly, they will bunch up and spread out momentarily all the time, so at any given instant there may be zero or many more than one $X$ atom/molecule per tiny cube.)  Real mixtures in the liquid state often have at least some nonideality, e.g. even in a dilute solution of $\ce{NaCl}$ in water, you will find "structure" in the solution, with the $\ce{Na+}$ cations and $\ce{Cl-}$ anions surrounded by a fairly fixed arrangement of $\ce{H2O}$ molecules, almost like a tiny piece of clathrate, so a mental arrangement of tiny boxes is an even less accurate atomic-scale description of the solution.

In short, the percent by volume description of a mixture is only a way to characterize the amount of material that goes into it, it is not intended as any kind of implication of what the  mixture looks like at the atomic scale.

As for why NASA reports the composition of the atmosphere by percent by volume: probably because it's closest to the actual experiments done to measure it.  You would typically measure the composition of a gas mixture by physically separating it (e.g. by lowering the temperature until each gas liquefied) and then measuring the volume of each component.  You certainly could from those measurements easily calculate a percent by moles, but – why?  You introduce a calculational step between the measurement and what you report, and scientists tend to prefer getting original data, right what comes from the instrument, if possible, as a way of avoiding even the smallest risk of some error introduced in calculation.