“Is this it?”
It is. That would have been considered a good touch-down even WITH landing gear.
That is the audio. The video is some other footage sync’d up to the audio. (There is a note a few seconds in saying “not original footage”)
I think this is the article and video I first saw, but I’m adding two others of this incident and there may be more:
17-YEAR-OLD STUDENT PILOT LANDS HER PLANE WITHOUT A WHEEL!
https://www.youtube.com/watch?v=B229-KLudTo
17-Year-Old Student Pilot Lands In Beverly After Losing Wheel During Takeoff
https://www.youtube.com/watch?v=22K4WTNkeOY
17 Year Old SOLO STUDENT PILOT Loses Wheel on Takeoff
https://www.youtube.com/watch?v=kZ5q7Iv5wTM