They drove away many of their best software developers, forming competitive software companies such as Activision and Imagic, and then spent resources trying and failing to sue them out of existence. Also departing were hardware folks like Jay Miner and Joe Decuir, who would be major contributors to the Amiga, an opportunity that Atari would later have in their hands and throw away. They completely muffed the next-gen console release with the Atari 5200, which was basically nothing more than a repackaged Atari home computer (already 3 years old at the time of the 5200's release), crippled by a terrible analog joystick that didn't self-center and was prone to breaking. They rushed VCS games to market assuming they would print money regardless of quality issues. After 9 months of raking in over $300m in profits in 1982, they ineptly handled the warning signs of Christmas 1982, leading to over half a billion in losses in 1983.
There was no way the crash of 1983 wasn't going to hurt Atari, but IMO a company which had been better run could have survived. As it was, without somebody that had Tramiel's level of discipline at the helm, Atari probably would have died in 84 or 85.