Atari was in serious financial trouble and  Warner had begun a desperate programme of layoffs and restructuring in 1984 (thousands would loose their jobs as entire departments were cut and projects cancelled).  When the deal with the Tramiel family was concluded with Warner on July 2nd 1984, they continued re-structuring the entire organisation as quickly as possible in a dramatic effort to stop the company loosing money - and if it didn't do it quickly, any chance of rescuing the company and its brand would be lost.  This included closing the Atari Inc. European HQ in County Limerick Ireland where 250 people worked, in fact, thousands lost their jobs worldwide as Jack and family reorganised their company for the launch of a new line of computer systems.  Atari employed over 10,000 people in early 1984, it would have only 1,750 employees in 1985.

As part of the deal, Jack Tramiel broke Atari into two entities.  Jack didn't want the Arcade Division of Atari (the part that was actually in profit) as this wasn't part of his future plans with the new company.  

Warner kept the Arcade division (later selling it to Midway Games Inc.) and the rest went to the Tramiels'.  

AtariTel was kept by Warner Communications and later sold.

In retrospect, the Arcade division would have been better kept as part of Jack's new Atari, not only because it was making money, but it would serve as a direct line for Arcade game conversions for it's own video consoles; it would have been especially helpful for the Jaguar launch which would take place almost 10 years later - but that's another story.

The rise and fall would continue, but it was now called Atari Corp.