How does the use of the word usually somehow mean I don't believe it? Balloons usually go up when they are filled, as they are usually filled with something that lets them float. However, sometimes they fall because they are filled with something that doesn't allow them to float. Admitting that doesn't mean I don't believe the original statement is true.
And novels, like games, are not just made up of one singular component. They are, as you yourself stated, made up of several, such as setting, characters, and the narrative style. And book series often have changes, both large and small, to their narrative style, and yet remain direct sequels to the previous books in the series because of the setting and characters being the same. Similarly, games can changes their gameplay, and yet still remain numbered sequels to the series due to sharing the same setting and characters. As in the case of Fallout, Metal Gear, and Final Fantasy.
Your anology would hold merit if talking about board games like chess, or checkers, or early games like Pong or Tetris, which existed as nothing but gameplay, and thus any change to them would change them entirely because they are definable by only one thing. However, games have evolved over time to add narratives, which changes the equation entirely, just like how early movies changed from just slides of animals running an the like, to what they are today, thus trying to hold today's movies to the same standard as those early ones is wrong, as they are not the same thing.
Changing a part does not change the whole. Changing gameplay doesn't somehow make it not Fallout anymore.
Redguard played nothing like the other Elder Scrolls games, yet remains one still despite it. Why? Because of its lore and setting. The most devout of TES fans came for the gameplay, but have remained loyal over the years because of TES's rich and wacky lore.
And don't you mean you can't accept it because it doesn't follow what you believe is the core series? Many of the original creators of the series have voiced their approval of Fallout 3/NV as Fallout games, despite their changes in gameplay. Who are any of us to say they are wrong?