Why is there no label manager in the pictured application of ArcGIS for Desktop?
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That's ArcScene, not ArcMap, and as such has no real labelling abilities. However there are plugins.
See this plugin for one potential solution: http://edndoc.esri.com/arcobjects/9.0/Samples/3D_Analyst/Visualization/ArcScene/Text_Toolbar/LABEL_3D_TOOLBAR.htm
And also this answer: How to easily label point values in ArcScene?