New Vegas is related to the source material in innumerable ways. Perhaps perspective, combat mechanics, and the inability of anyone in the wasteland to ever forgive any transgression against their faction are integral to a Fallout title to you, but to others, sharing a writing style, design philosophy, canon, and continuity were more than enough, especially considering it was the first game in the series that's shared those things with Fallout 1 and 2 in a decade.
But these latter points are not gameplay. It's the same with the Warhammer games; they share the setting, canon, continuity... reasonably enough, but they are unrelated games aside from the IP setting. Spacemarine does not have the gameplay of a Dawn of War sequel, nor vice versa. Of course they are not trying to either, but the point was about the belief that a mechanically unrelated game [skinned in the same IP] was a superior example of the concept; perhaps even a better example of how the original
should have been, had they been able to at the time... but that's intrinsically false when the new gameplay ignores, or even opposes the original concept.
In New Vegas' case, they were certainly under Bethesda's thumb, and forced to use FO3 as their foundation. What they did was outshine Bethesda at their own game; using their own toolset. But it was still FO3.1 in terms of mechanics. They added some neat features to it, but it was at most a half step in the direction of Fallout 2.
Imagine a TES 6 that surpasses all previous TES games in writing, lore, interactivity, and customization of the PC... but mechanically restricts to a class, and limits the player by their past choices in the various guilds; and for that matter, is seen in fixed isometric. It would miss the mark on all aspects of the series gameplay, and core concept.
As established in this thread, there are a lot of things New Vegas does better than Fallout itself, some of them at the heart of the series' design principles. To argue that none of those things could possibly qualify it as a superior Fallout game simply because of the engine and POV differences is to argue that it couldn't even be a better Fallout game than Tactics-- or Lionheart, for that matter.
I am fine with the engine [Gamebryo], just not fine with how it was used for these Fallout games.
Loki uses Gamebryo as well; a contemporary of TES:Oblivion
*Not turn based, but it certainly could have been, so it's easy to imagine Van Buren or the Troika Tech Demo running on the Gamebryo engine.