He said it more than once, and clearly said project one of those times. He also gave context that made it quite clear he was talking about the project.
He made it pretty clear that he was quitting "that job" and going to study more bioinformatics. As far as I know Google doesn't do a lot of bioinformatics. Peppered with a couple of his midlife crisis comments it seems like a fair assumption that he was leaving Google. At no time in the video did he explicitly say that he was staying.
Disagree. After watching the video, he talks about the project, mentions quitting "that job", and then the speech is over. Not that any of it really matters - but the statement in the video is confusing.