You seem to be confused (which is fair, this is a little confusing). In 1984, Warner Communications sold Atari's home and computer game division to Jack Tramiel, which became Atari Corporation. Atari Corporation was the company that made all the future Atari consoles (7800, Jaguar, etc) and computers (ST line). Atari Games, Atari's arcade game division, remained with Warner. This article is entirely about Atari Games, who had nothing to do with anything sold for the home market with the Atari name. They were entirely separate companies. The reason why they did business as Tengen was that as part of the split, Atari Games wasn't allowed to sell games to the home market using the Atari name.

I will say that the article is a bit inaccurate at the end. Atari Games kept using the Tengen name for several years after the lawsuit for publishing games on the Genesis. They only stopped in 1994 when Warner consolidated all of its game related brands under the "Time Warner Interactive" name.