I go by the industry norm for a description of a new vehicle or new generation. That is the body or chassis must be changed significantly. In this case the chassis is the same and the body is the same (with a new hood). I know of no car in history that was considered new based on a new powertrain alone. For example the Corvette C2 started with a 327 and ended with a 427 and was still a C2. Much bigger change.
For the Viper it seems people want to designate things for personal reasons. Whether it is to help sales (read marketing) and show newness or improve personal vehicle value (read owners). I do know that when the 2003 was started Team Viper tried to state it as "Chaprter 2." That is 2nd generation. Unfortunately, so many owners used Gen 2 for the 1996 Coupe the Chapter 2 version did not hold. For the 2008 they started to call the engine the 4th generation of the engine. And that would be quite accurate as the 1992-1996, 1996-2002, 2003-2006 and 2008+ have significant differences in the engine (blocks, heads, etc).
But now that the Gen 4 name has been firmly established I reluctantly am going along with it. Consistency is also important.
This is coming from a powertrain guy (engineer in powertrain for what seems like an eternity) and someone who believes the engine is the core of an automobile.