Q:

What is the elevation unit of the Natural Earth's Shaded Relief raster? 

I need to use this raster data to extract elevation for points and polygons, but I am really confused about the unit of the pixel values
http://www.naturalearthdata.com/downloads/10m-raster-data/10m-shaded-relief/
The pixel values are between 49 and 252, and oceans have higher pixel values than some land areas.  How should I interpret the pixel values and convert them to meters? 

A:

You can't get heights or depths from a shaded relief raster.  The purpose of shaded relief is described in this tutorial:

Shaded relief models indicate terrain displacements using a shadow
  effect from evaluating the aspect  and slope relative to the sun's
  azimuth angle and altitude  achieved with varying grey scale tones
  resulting  in the darkening of one side of terrain features, such as
  hills and ridges (the darker the shading, the  steeper the slope). 

The tutorial is worth reading.  There is also a dedicated web site about shaded relief http://www.shadedrelief.com/.
For getting the real elevation values you need a digital elevation model (DEM).