When you copy a diagram directly from yEd into Word, Word will most likely embed an EMF graphic of the diagram. EMF is a very limited format that does not support many types of gradients and transparency and has poor support for text which in turn results in low-quality representation of diagrams.
For high-quality export, choose SVG as export format. Unfortunately, Word does not support SVG import/display.
The next best thing to SVG export is PNG export at zoom factor 1. As long as you import the PNG image at its original size, it will be displayed fine. If you scale the PNG image up or down, this will result in a loss of quality. This is actually not a Word (or yEd) short coming - PNG (and all other types of raster) images cannot be scaled without loss of quality.
