The problem is not in the licensing or action of the export function. It is a matter of understanding how the Export Raster
function works.
Based on your description, you are trying to select some number of cells from the raster, then do as you would a standard feature class in ArcMap and Export using a right click on the Layer Name.
If you did this on a Featur eclass with features selected, the window that comes up would look like this:
By default, the "Selected Features" option is used when there are features selected in the layer.
Rasters work somewhat differently when you export them. Here is the export window on a Raster, showing the Selected Graphics
option grayed out, as you mentioned.
This Help document explains about Exporting a raster in ArcMap. In it, you see this section about Selected Graphics:
The Selected Graphics (Clipping) will clip and export the raster
dataset based on the selected graphics in the display; this option
will retain the data inside the graphic. Alternatively, you can check
the Clip Inside option to remove the data within the graphic and keep
the rest of the data.
What this is referring to, is not about selecting specific records
from the attribute table that you want to export, but rather selecting a graphic
in the Data Frame, that you want to clip your raster to, like the polygon below:
You can create Graphics with the Draw toolbar (more information here).
Right clicking to export the raster with the graphic selected, gives you the following option enabled in the window:
If you do want to Export Records from your Raster Attribute Table, you need to follow the procedure from this Help Document: Exporting a raster attribute table
Best Answer
Your data is probably not projected. This means that inside the shapefile, the vertices of your polyline are stored as decimal degrees. Usually, you would have to use the Project tool to project the dataset into a planar spatial reference system that allows for geometric calculations in non-angular units. However, when calculating line length (but not area), ArcGIS can calculate the geodesic distance, which should result in an even more accurate result.
So instead of using the "Calculate geometry" tool, use Field calculator, select the "Python" parser, and enter the following expression: