But the thing I'm wondering about is what do I need to make a game... APIs, game engines, libraries etc to make a very basic game. (And whether I even need them... it's 2D btw.)
What you need is what's already been said: a language that you know and a compiler/IDE in which to use it. And then, you'll need experience coding. You need nothing else. You can and in many cases should use various APIs, engines, libraries, etc., but you don't need any particular one. Which ones are even options depends on what specifically it is you'd like to make.
From the information you've provided so far, I'd say SFML is a great library to use. C++ is fine, though I think you'll get off the ground more quickly with C#.
Beyond this your question is pretty vague, which may be why the answers you are getting don't appear to be quite what you're looking for. If you want to code your own game (as opposed to using game-making software) you're going to be building just about everything I think you mean by "game" by yourself and out of nothing. Have you designed any specifics of what you want your game to be yet? If not, doing so will really help you break down the tasks that you still need to do.
A good first step might be to open a window. Does your game use a GUI-style menu? Sketch out some ideas on how you would do that using your language of choice and any libraries you plan to use. How you start a game is the same as how you make any other part of it: you identify a task that needs to be done, and you figure out a way to code it up. It's always overwhelming at the start, and getting to work is the only way through.
but the tutorial doesn't even tell me
This strongly suggests to me that a 2D game might be a bit advanced of a project for you right now. It's not that you can't do it, it's more that people tend to radically underestimate how much stuff there is to do to make the game they're imagining. You'll know your experience level better than any of us. Have you done much coding yet? If not, a simpler game might help you get a handle on the game-making process without seeming so daunting.