As Mary Travers notes in the video, the group had sung the song at almost all their concerts for decades, so it was a particular thrill for them to perform it with Seeger.
For the most part, Seeger only accompanies them on his banjo. He sings along on occasion, but doesn't have a microphone, so his singing doesn't come through much. Late in his life, his voice had not been strong, so it's possible that he preferred not to have a mic -- though it's also possible there just wasn't one set up. Though I suspect the former, since he could have just stood by one of the other microphones.
Making the performance all the more touching is that if you look closely, you'll see that at this point in her life, Mary Travers had a cane with her for support.
Whatever their ages and conditions, it's a wonderful piece of touching history to have.