Someone other than Steven or the player character wins in the "good" ending.
When the player character touches Steven, it destroys them both but the phlebotinum
reaction gives birth to a new character who promptly uses the box to go back in time and set the game in motion again.
The ending is all about looking back into childhood, and rediscovering dreams.
Think about it. In the good ending's credit roll, it is said that someone (hopefully the player character) had a box in which he painted whatever he dreamt of. At the age of 10, light (a grasp of reality) came, and he realized that if he settled for one of those dreams, he would have to give up the others, therefore "killing" them. Trauma kicked in, and he tried to never ever think about it again. Then, fully-grown, the player character finds himself in a pointless life because in childhood he couldn't deal with the fact that you couldn't have all your dreams accomplished, and gave up dreams altogether. Then he finds his childhood box, full of dreams and alternate realities. As he looks through them, his memories of his inner child, repressed because of the trauma, come back. He develops Steven. At the end, he is able of not taking the pill (trying to escape again), and face Steven. His years have made him more mature, and he accepts that he cannot achieve every dream he ever thought of, but instead he can focus on one of them and accomplish it. By going out of the box, he remembers how unfortunate was his life, and how much the box helped him, wishing he could go back in time and tell himself to get over that way earlier. At the end, as he runs he duplicates himself. Every one of his copies belongs to a different dimension of reality, but in everyone of those he has settled for one dream, and nothing will stop him on his way.
- Tying into this, the tone of the Third Ending suggests that Steven is desperately trying to prevent himself from "dying" by refusing to stop writing the message. This could be taken as a metaphor for keeping one's inner child alive through art... a possible Author Avatar?
Edmund confirmed it, but how did it come to this?
- One of the endings in the Rebirth remake show a "Missing" poster with Isaac's face on it. It's possible that he finally escaped Mom, though the jury is out on whether he's still the Anti-Christ or whatever.
Steven is writing the letter to himself to prevent his time line from collaspsing.
At this point in the game time itself is starting to get a bit fast and loose with its rules. On one hand we have Steven escaping the box and going on to become the player character who then goes in the box and gives birth to Steven (or something). On the other hand we have all the time clones popping out with you, rather then Steven exiting earlier to become you or you exiting to put yourself in the box. I believe that the Steven who is sending the message to himself is the remnant of the ending where you fuse with yourself, unable to fulfil his timeline of exiting the box. Since he never leaves the box in this timeline, there are no time loops to warrant its creation and so it is falling in on itself. Steven is sending one last text to keep a connection to a timeline that is not invalid and therefore retain some level of stability. He spends his last moments cursing you and him (or whatever) out for triggering this fucked up ball of time-whimey bullshit by originally pushing yourself in the box and thusly "killing" him. He stops the message and loses his one connection to a valid timeline and therefore dies. Maybe he lost the connection, maybe he runs out of battery, maybe he loses the will mid-sentence, we're just not privy to this timeline.
Throughout the game, Steven constantly communicates with other versions of himself. The surface level is that these "other Stevens" are alternate timeline counterparts of him, but due to the metaphorical nature of "the box" and the game, it's much more likely these are other aspects of Steven's psyche. Some Stevens are very amiable, while others are downright hostile (including the one that first forces him into the box.)
Furthermore, if one considers that "Steven is Isaac", then this would come as no surprise, as the various playable characters in Isaac also represent different aspects of the boy's personality.
The "Good ending" of Chapter 1 could then be considered a Split-Personality Merge?