Well, I never played the game, but considering all the hints you are dropping in your question I'd say that the game was, nearly certainly, following the storyline of...drums rolls...The Death of Superman :-D
The entire storyline of The Death of Superman included both his death (by graceful courtesy of Doomsday), the appearance of four new "Supermen", and, finally, his resurrection (of sort).
The exact story arcs, in publication order, are:
And about your list:
Well, the man himself. The one who fights Doomsday. The one who dies (nearly).
Uh, yes, Superboy. A clone of Supes created by Cadmus. A partial clone, because good luck obtaining the DNA of Superman, so the original DNA had "holes" that were filled by Cadmus, hence his powers are partially due to a form of telekinesys.
Man of Steel
John Henry Irons, AKA Steel. First a top level scientist, then retired to be a constructions worker, saved by Supes one day, he decides to take the mantle on his shoulders after Superman death.
I think you may mean Eradicator, aka the Superman With The Visor. I'm not going to write a synopsis of it, too, because it's way too long and convoluted. Let's just say it was a kryptonian probe tasked with the mission of preserving the Kryptonian lifestyle.
Hank Henshaw, often just Cyborg. Take the Fantastic Four, have all of them except one die instead of getting incredible powers, and have the one who survives thinks it's Superman fault. When Superman dies, he decides to take his revenge by pretending to be him reborn and then destroy his reputation.
Superman in Black
Our big blue boyscout himself, recovered from his death, only this time in a temporary suit which is basically his kryptonian hospital pajama, and a legendary mullet.