Thanks for your reply, Adrian!
However, the problem was that the z-values were not in the attribute table and only visible in ArcScene.
But I figured out a work around:
1) Convert the polygon vertices to points (tool: feature vertices to points)
2) Enable 3D of new point data set using DEM (tool: interpolate shape)
3) Add z-values to attribute table of new point data set (tool: add z information)
4) Calculate standard deviation per polygon in a new table (tool: summary statistics)
5) Join table to original polygon data set