“While the defendant pled guilty, our office does not have a plea agreement with him,” the U.S. attorney said. “There are no accommodations or concessions, and we are free to seek the maximum penalty under the law.”
There wasn't any plea deal in place, he (in consultation with his lawyers) probably figured this was the best path for him to possibly not get a life sentence. It's as simple as that.
I've seen the stalking charges described as "stalking resulting in death", which I suppose is worse than plain old stalking but not quite murder. Regardless, he's facing a max sentence of life. It seems like he's taking a gamble that he will get less than that.
And as far as I can tell, he is betting they by saying "I killed him" as part of this plea in this trial, he can get out of the state trial.