In case you just want the important points:
Dawkins said he had a hemorrhagic stroke (not the ischemic kind that would affect the brain).
It was the result of stress-related higher blood pressure, which he says he may have had as a result of recent controversy, including being booted from the NECSS conference. He added, however, that on February 5, he received a letter from conference organizers apologizing for disinviting him and asking him back to the conference. (I’ve asked NECSS to confirm this, but have not heard back as of this posting.)
One thing he didn’t mention? God.
He didn’t say this in the audio, but Dawkins has said before that he wants to make sure there’s a tape recorder near him when he’s on his deathbed, just to confirm that he didn’t turn to God in his dying moments. While he’s thankfully not quite there, this audio confirms he’s as Godless as he’s always been.