While most of these home arcades aren't discontinued yet, the rise of third-generation home arcades next year would eventually put an end to their popularity.
~100,000 units - Emerson Arcadia 2001
Little more than a footnote in video game history, this home arcade barely lasted two years on the market simply because it had nothing to offer in comparison to the other big firms.
~750,000 units - Fairchild Channel F
While it sold poorly in its day, the Channel F has been well-known among video game historians as the first home arcade with programmable ROM cartridges, as well as the first invention of Jerry Lawson.
~3,000,000 units - CGE/Milton Bradley/Hasbro Vectrex (first generation)
The latter half of the decade would see Hasbro's rise in the home arcade industry, but the original model Vectrex merely served as a humble beginning for Hasbro's electronic gaming division.
~12,000,000 units - RCA Studio 2
While declining sales at the end of the Studio 2's lifespan would put RCA in an uncomfortable place, the home arcade was still regarded as a success - not to mention how revolutionary the Master Strategy series has been. As for Jerry Lawson, he decided to step down from his position and become a freelance inventor like Ralph Baer did. His desire to do this was an open secret thanks to the Wonder Clock[1] being invented during the Studio 2's lifespan. By 1984 RCA announced that while it would continue to sell the Studio II for at least one more year, it would slowly be phasing out its home arcade division. Video game fans were disappointed by the news, but RCA would find success once more by entering the camcorder industry in 1985.
~13,000,000 units - Mattel Intellivision
Mattel had only been in the video game industry for around half a decade, but the overall success of the Intellivision proved that this would be a profitable industry in which to stay. While not spinning it off, Mattel would eventually use INTV as a cover-all label for their home arcades.
~16,500,000 units - Coleco ColecoVision
Quite surprisingly, Coleco managed to pull a 180 from the Telstar series and become a driving force in the early 80s' video game industry. Back in 1984, nobody would expect Coleco to go back down, but, in hindsight, some things just couldn't be predicted.
~35,000,000 units - Atari (12,500,000 VCS, 22,500,000 SuperSystem)
Atari would end up on top this generation, but only because they jumped ship in the middle. The goal of the SuperSystem is the finish what the VCS started before the VCS was dragged under the bus (even though Atari themselves would drag it under the bus as well). Overall, Atari has become a household name, and would use that status to prove themselves viable in the next generation.
Notable third-party companies:
Activision
The company behind the Pitfall series have been doing well since its breakout in 1982. Activision has exclusively published for Atari, but the third generation might change that.
Imagic
Founded by ex-Atari and Mattel employees, Imagic would find success in their multiplatform game Demon Attack. No crash ITTL means the company has a chance to survive the rest of the 80s.
Namco
Ah, yes, the company responsible for the nationwide Pac-Man fever. Namco is often cited as the reason why arcade machine still thrived through the early home arcade industry, with hits debuting in the arcades before being ported to said home arcades.
Nintendo
While games like Donkey Kong and Mario Bros. proved to be popular in both arcades and home arcade ports, the Japanese firm has planned to unveil their third-generation home arcade/computer hybrid, the AVS, at the Winter CES of 1985. Time will tell if it will catch on.
Sega
Much like Nintendo, Sega would also be planing their break into the USA, although plans are a bit foggier. Their plans to find potential business partners involved demonstrating the SG-1000 to various firms - and in a surprising turn of events, pop star Michael Jackson expressed interest in investing in Sega of America. Alas, it was not to be: the late pop star experienced severe third-degree burns [2] in an accident while filming a Pepsi commercial, and the complications of these burns have led to his tragic passing in early 1984.
Taito
Like Namco, Taito would find more success in arcade machines than home arcade ports, with hits such as Space Invaders, Mr. Do, and Qix.
[1] This was an alarm clock that would allow parents to record a wake-up message and have it play as an alarm, famous for being endorsed by Stevie Wonder. Lawson did develop this OTL, but ITTL it made it to production.
[2] As opposed to second-degree burns OTL.