Delta Milage run from LAX>PVG PVG>LAX

Unfortunately, you do need a visa. Simply speaking, your itinerary is a round trip flight and that means that you need a Chinese (L) visa obtained in advance. Also, you should be aware that you will not be allowed to board the plane in Los Angeles in the first place if you appear without a visa.

Since you are a mileage runner, you are advised to apply and obtain a 10 year multiple entry Chinese tourist (L) visa. Indeed a good investment for US citizens that travel more often to China. The alternative is to adapt your itinerary to be eligible for 24 or 144 hour visa free transit by introducing a third country. Something like this:

Los Angeles - Shanghai - Seoul - Los Angeles