Greg doesn't wear his magic suit or have his magic wand with him. He used Anthony and Murray to help.
Greg, Anthony and Murray stand around an empty glass box. They can hear someone snoring inside the box, but there is no one there. The Wiggles cover the box with a drape, say the magic words, and when they remove the drape, Jeff is inside the box. But he's asleep, and the Wiggles need him for the next song, so they wake him up.
In a concert photo from late 1995 or 1996, the glass box is seen on stage as The Wiggles perform Can You (Point Your Fingers and Do the Twist?). This could suggest that The Wiggles performed the magic trick in concert.