Yngwie doesn’t over-use shredding. He’s awesome at everything, and shredding just happens to be a small part of everything. His use of vibrato and other expressive elements along with his ear for melody and harmony is the best there is, and I can’t name one guitarist living or dead whose tone I prefer vs Yngwie.
Rather than just disagree with everyone I’ll try to shed some light on how to listen to Yngwie. Think of most of the first couple of minutes as foreshadowing, just like an author might use. If you listen to the song twice in a row, which of course I recommend, you might find that everything makes so much sense from that perspective. Instead of hearing puzzle pieces that don’t fit, you should start to hear a complete picture. I would also bet that most or all of the lead guitar in this song was improvised, although of course I can’t prove that.