Your point has merit of course, but it is not really cogent. The semantics of the word "storage" are largely arbitrary, but I suggest that the most nearly essential attribute is that one begins with some entity and eventually recovers that entity.
Consider a tent for example: among many possible definitions we could call it a dwelling, in particular, a portable dwelling. So let's port it! First, we knock it down, fold it up, and in doing so reduce it to anything but a dwelling except possibly for a few enclosed cockroaches. When we reach our destination we unfold it and re-erect it.
Now, would you deny that we had stored the tent, on the grounds that during its storage it had not been a dwelling? I think that is rather special pleading.
In a delay line storage device a modulated beam of light is ideally not changed at all, either in frequency or in modulation. The fact that it is moving does not seem to me a persuasive argument for its not being stored. Certainly the data, the information, is stored, unless you have some argument to the effect that moving data is not stored data. Suit yourself on that point, but it is just possible that you might be in the minority in insisting on any such convention.
It certainly is true that stationary light is something of a contradiction in terms, much as warm ice would be. Where I come from, ice, on being warmed, turns into liquid and putting it into a glass to prepare say, whiskey on the rocks, would not satisfy most clients. Accordingly, although I could store the water content of ice, if I did not store the ice cold, I could hardly claim to have ice in store.
Similarly, although I could store either the data from a modulated beam of light, or its energy, or even both, permitting me to regenerate a reasonably equivalent facsimile, to claim that I was storing the light itself would be a rather peculiar argument if the light were not moving, any more than the ice would be ice if it were molten.
In short, I don't see why storing something in a mode that maintains appropriate aspects of its nature should not be called storage simply because it is not static.
But by all means, if this does not strike you as reasonable, please do not feel constrained to adopt my personal preferences.
Cheers,
Jon