You are right. A shadow is not a part of a logo, it is an effect applied to a logo.

Effects that will have issues not only when printing, but also when scaling, like thin lines or super small elements are a bad choice.

A logo is different than an illustration. A good logo can be later represented as a 3D object, as an animation, carved in wood, represented as an icon, as 1 color, etc.

But that does not mean that you often need different versions of it. The obvious idea is a vertical and horizontal version; a normal-sized version and a simplified icon for an app.

On your case, yes, it sounds fishy the fact that a gradient needs to be represented as lines in one version and a gradient in another.

When you screen a gradient for print (offset, silk print, etc.) you transform that gradient into dots, either different-sized dots or small dots with different densities (numbers) but that is part of the print process.

If the lines are a good solution, they should have been part of the design, but to indicate part of the idea, speed, transformation, etc.

If they are only there as an effect, as a shadow, that is not part of the logo.