While I disagree with their ranking (obviously) I actually think the intro to fallout 3 is decent. It checks all the boxes:
-a decent intro to this part of the world and some of the characters
-various options for different playstyles are available
-choice and consequences in the short and long term
When you consider the intro sections to the other games, it really doesn't look too bad. Fallout 1's intro does a great job of setting the atmosphere and tone of the game but is very rudimentary gameplay wise. Fallout 2's is a chore plan and simple. New Vegas' intro is just fetch/kill quest but it does do a good job of introducing the player to the mechanics and leading into the first real sidequest. Fallout 4's intro is just walking around killing radroaches.
I have to disagree with most of these points
Fallout 1's intro is almost perfect. The story is simple but effective, everything is clear but at the same time vague enough to give the player a vast amount of freedom in creating their own backstory. The cave segment is so short but manages to teach new players all the basics of the game mechanics and, most importantly, doesn't feel like it's teaching you at all. It feels like you've been thrown into deep waters right away but the invisible hands of the designers are looking after you. Also, a great feature is how when you play for the first time, your knowledge of the world is almost the same as your characters - you know that the world is a post-apocalyptic wasteland and is probably a dangerous place, but what exactly awaits you - you don't know. You have no idea of what creatures, factions, cities etc. are out there. Fallout 2 kind of dropped the ball here - for example, your character should know where the hunting grounds of Arroyo are, but you don't so you have to ask your cousin and he looks at you like you're an asshat - way to throw the player out of the character at the beginning.
The only flaw to F1's story is that your character is artificially forced to save the vault - but the fact that I consider this a flaw is a true testimony to how well the game is designed, as most RPGs are like that and nobody even bats an eye.
New Vegas did this aspect better - as someone here mentioned, your character just has no choice but to go after the package as it's safe to assume that they will soon be dead otherwise. That could have been emphasised more, as most players probably missed it, but it's there.
Fallout 3's intro is absolutely horrible, it's so bad I have no words. Not only does it deprive the player of any role-playing freedom, it lasts for an hour and feels like watching a cutscene. A bad cutscene. The idea of playing as a baby playing with toys in a Fallout game is pretty shit already, but the birthday scene is where it's at. It's a real cringe-fest. The writing and game design are just horrible there and I could never help but wonder what the fuck are these scenes doing in a Fallout game. The GOAT test is a pretty stupid idea but it does prepare the player for Bethesda's attempts at humor so at least you know what to expect for the rest of the game. All of that could have been cut and the game would only gain from it, there's not need of so much pointless fluff just to teach you how to draw a gun and shoot. The worst thing is that character creation is built in into all this crap. Maybe it's just me but I hate the fact that I not only can't adjust my attributes and skills at the same time, but also there's a 20-minutes gap between them (New Vegas fucked that up, too)
After the game wastes 40 minutes of your time, you finally get to do something. The escape from the vault teaches you that the game's moral dilemmas are as complex and deep as those from Winnie the Pooh and that you shouldn't expect having much impact on the world. You pretty much always do the same - kill some guards, wear their armor and exit the vault, optionally helping Butch and talking to the Overseer on your way. The various playstyles you can choose are killing enemies with guns or killing enemies in melee combat and you can sneak past some of them. These bare almost no significance on the game.
Yes, it introduces you to the characters of the vault, but they cease to exist one hour into the game, except for one sidequest later. So what's the point?
And the worst thing about that intro is that when it finally ends, you're still playing Fallout 3
Yeah, if 76 isn't a RPG of any sorts then neither is Fallout 4. Fallout 3 and New Vegas are what I'd call action-RPGs but one of them is vastly better than the other one through choices, consequences, writing, and general understanding of source material.
Fallout 3 is not an RPG. It's like calling Doom an RPG because you role-play as a space marine