In Roman languages, the word "engineer" derives from the word for "wit" (e.g. "Ingeniero" <- "Ingenio" in Spanish); hence there's a mental connection to identify an engineer as someone who uses her wit to solve problems. The Product Engineer hence uses her wit to solve Product issues, that could range from technical issues to manufacturing, materials, distribution or even marketing issues. She has to have a more holistic and less deep view of multiple areas, a la Project Manager.

Now you'll tell me that I'm talking about a Product Manager and I'll have to agree. In my opinion, a Product Engineer is a different name for a Product Manager. Product Management is a really broad area and I think some people more inclined to technical stuff and especially software development would feel more at home being called Product Engineer than Product Manager.