osgEarth has limited "GIS-like" styling capabilities. Your screenshot is OSM data rendered using Mapnik (or something similar), rasterized on the server and streamed as image tiles. If you want something that complex you will need to take that route instead of trying to style at run time in osgEarth.
osgEarth can draw simple text labels (see feature_labels.earth for example) but it will not draw text following a street vector. It also cannot fill a polygon with an image. Features like these could be added, but at some point it will make more sense to do it on a server.