The New 3ds is a 3ds model. The improved hardware is just used to run existing 3ds titles better and allowing some exclusive wii ports.

What if it has other exclusives?

It's still too little. Gameboy Color and dsi also had some exclusives and they remain as new versions of the gb/ds. I don't even know why people start discussing things like this.

I don't really go by exclusives. New 3DS's hardware is heavily based on the architecture of the original 3DS, just with more CPU cores & RAM. For something to be a full successor, it would have to be something drastically different. I don't see New 3DS as any different from the DSi, both were just a slight upgrade on the hardware of the original machine.

It's a new console. It's a new 3DS model to be more precise but it's still a console. And it's new, so I'd say it's a new console.

Like a new console... This is like defining what a "kind" of animal is. You just know. Dogs and Wolves are the same kind. Dogs and Humans aren't. The New 3DS isn't a new console. Something like a Wii U is.

Generational hardware leap forward or something else very significantly new that leaves a large imprint on the industry. 

Been that way basically every console generation.