As is (the) tradition

At the beginning of the clip, Jimmy Kimmel said:

It was too late. John Robers, the Chief Justice of the Supreme Court, as is tradition, did the honors of swearing our "Celebrity Appresident" in.

Is this transcription correct?

If so, "as is tradition" could have been replaced with "as is the tradition" here?

If so, is there any difference between the two phrases?