He's been saying he doesn't want the job, but did you read the article? He brought up on his own the idea of a reality show host taking over the Dems; and when Mehdi Hasan (his interviewer) asked if he meant himself, Stewart didn't deny it. Didn't push back.
Just chuckled.
It sounds to me like he's reconsidering, and testing the waters.
I certainly think he's shown amazing leadership ability.
He's always expressed an active disinterest... but in the interview the article's talking about, he brought up the possibility of "the right reality host" taking over the Democratic party on his own. Then didn't deny it or push back when the interviewer asked if he meant himself.
That's the most positive I've heard him be about the possibility.
He spent a long time as producer and director on The Daily Show as well as it's host, and it looks like he's got some other producer/directory credits as well.