By the article, the “small Piper” was carrying: a 61yo man, his wife, their three daughters, an employee, and “several others.” That’s nine or ten people. If they had any baggage, that’s all the more weight. Sounds to me like the craft was overloaded.
Yes, what small Piper airplane can carry 10 people or more?
Sounds like somebody had some very bad judgment somewhere.
It was a Piper PA-42 1000. Twin Turboprop. Crew 1-2. Pax 6-9.
It could have handled that load theoretically. But it would likely be near max load if not over.
If not over, any engine fault, any climb would be impossible.
So yea, probably an overload condition.
The Piper PA-31 Navajo Chieftain seats 10 and is a twin engine. Small, maybe in comparison to a commercial aircraft? But among private pilots it's a pretty big plane.