Allow me to present my own scenario.
Based off of the Nintendo-Atari negotiations of 1984...
Atari doesn't decided to off the negotiations, and Warner sticks with the company a little longer, allowing Atari to, in 1985, release the Atari 7800 ProSystem and Nintendo, with Warner's funding and Atari's support, to release the Nintendo Advanced Entertainment System.
Unfortunately, because of Atari being dictatorial, Super Mario Bros. is delayed so Atari can make it more appealing towards American gamers. In addition, because of Warner's reluctancy, both systems are undercapitalized, slightly buggy, lacking in many games, and under-advertised.
Thusly, though both are popular for the first year after their release, sales fall and despite a little bit of third-party support, it becomes somewhat unpopular.
Sega releases their Master System in 1986.
In OTL, Sega did not want to challenge the Nintendo juggernaut and instead contracted Tonka Toys to market the system. Tonka was an extremely poor marketer for the system as they had had no experience with electronic games before.
The Master System is marketed much more and Sega is happy to release games. They start the Team Sega Newsletter, a quarterly mini-magazine, to offer news of upcoming games and tips and tricks.
Due to third-party support and franchises like Phantasy Star, the Master System becomes a hit while Atari and Nintendo fall back.
The Nintendo system is discontinued just as Mario was about to be released. Nintendo, surprised, stays in its home market for several years while trying to formulate a plan for the North American Market.
Atari's video gaming division is sold to the Tramiels while the arcade division stays with Warner. The Tramiels, seeing Sega's success, begin to more aggressively market the 7800. But it is too little, too late, and the 7800 can not match the Sega juggernaut.
In 1988 the Team Sega Newsletter becomes Sega Visions Magazine.
In OTL, the Team Sega Newsletter did become Sega Visions, but Visions could never properly compete because it wasn't a proper magazine - it was just an under-funded Sega propaganda rag.
Epyx meanwhile develops a system but is unable to market it. It is offered to many companies... Atari accepts it.
For 1989, Atari releases the Lynx to little fanfare. However, because of its advanced capabilities, some people buy it. Nintendo soon releases the GameBoy, armed to attack the market with its games. NEC also releases the TurboGrafx-16, but due to its price and poor advertising, it is unpopular.
In 1990 Sega releases the system Genesis to the Japanese market, and it is shipped with Sonic Hedgehog, a new game with a new mascot to replace Alex Kidd. Other titles included Phantasy Star II and Altered Beast, among others.
Sega is quick to have it ready for the American market, where it is most popular, however, and allows two sets to be sold. The Beginner's Set includes the Genesis with Sonic Hedgehog, along with the necessary cords. The Master's Set includes the Genesis, along with Sonic Hedgehog, a Master Converter to allow the Genesis to play Master System games, and the necessary cords.
In 1991 Sega launches the Game Gear to compete with GameBoy. It comes with a conversion of Sonic Hedgehog. A Deluxe set carries a Base Converter to allow the system to play Master System games. NEC also launches a portable TurboGrafx in the form of the TurboExpress.
That same year, Nintendo launches the SNES. The launch titles for it in America include Zelda: The Adventure of Link, Super Mario Bros. World, PilotWings, and F-Zero.
Due to the SNES's amazing capabilities, Atari leaps at the chance and begins to more aggressively market the Lynx not as a handheld, but as a portable console, showing off WarBirds in commercials compared to PilotWings. This helps win the system many more fans and Atari begins to gain more market share.
By 1991, the share for the American console market is as follows:
Sega - 90%
Atari - 5%
Nintendo - 2%
NEC - 2%
The share for the American handheld market is as follows:
Nintendo- 57%
Sega - 33%
Atari - 7%
NEC - 3%
But Atari and Sega are gaining on Nintendo's head start.
Nintendo continues to fight the Sega juggernaut with a release of a remade Legend of Zelda, titled Zelda II: The Origin Adventure.
Sega meanwhile releases Phantasy Star III: Generations of Doom and Sonic Hedgehog 2.
Atari continues to advance its Lynx with a more development, due to a growing popularity. A game is in development called Guardians: Storm over Doria.
Meanwhile Sega Visions becomes monthly, Nintendo Power is launched, as is Atari Go!
1992. In the console market, Sega dominates and dukes it out with Nintendo in a fierce war.
In the handheld market, Nintendo barely manages to dominate while Sega and Atari advance.
Who will win these fierce wars?