and it's "just" a bunch of nested lambdas with no "do" in sight. What's different from "regular" code is that those lambdas 1) return IO actions, and 2) are strung together with monadic bind (>>=) to build one big IO action.
To be sure, in this case the do version is much easier to read (that's why "do notation" exists). It can be used with any monad, though - nothing ties it particularly to IO.
(>>=) is just an operator. The values that it operates on are anything with a Monad instance, just like the values that (+) operates on are anything with a Num instance. There is nothing voodoo about monads or about bind (>>=); such voodoo as there is lies solely in IO, which is interacted with the same way as other values (though certainly what you can do with (IO a) is more limited than what you can do with (Maybe a)).
I used to think that Monad was some alternative realm in Haskell, a realm where purity didn't exist and everything was written in an alternative, built-in language (do-notation). That's because people tend to refer to using Monads as "working in the X-Monad", as if it is some... place. But then it turned out... Oh, so it's basically just a signature/interface/type class.
True! But one neat thing is that, if you have a black-box abstract data type then you can force people to use the provided Monad interface if they want to do stuff with it. The IO monad does exactly this to create its "alternative realm"; there is no way to get "out" of IO once you get in , the only way to run an IO computation is to have it be directly or indirectly called by "main" and the only primitive way to compose IO computations is with the monadic combinators.
To be sure, in this case the do version is much easier to read (that's why "do notation" exists). It can be used with any monad, though - nothing ties it particularly to IO.