15 years ago... They had just released a remake in 2008 for the Xbox, so the IP was certainly fresh in their minds.

https://en.wikipedia.org/wiki/Battlezone_(2008_video_game)

Did they eventually drop the threat or did something else happen?

That's hilarious. God bless the old Atari who wanted to sue the world. The irony now of course is that Atari no longer own Battlezone's IP. Rebellion managed to grab it when Atari went bankrupt in 2013.