To see your child "all grown up" is one thing, but to see your child all singing, all dancing, and on live television while you're sitting in the audience with cameras in your face must be entirely overcoming. Therefore Bruce's tears were expected.
And if the cameras didn't quite catch his emotion, his other daughter Tallulah helpfully posted this to Instagram with the caption "Look at this cutie tearing up from my insanely magical sisters dance. We are all so proud of you Rue."