If the kid's point (I can't know for sure from only this clip) is that he will not recite the pledge until we fulfill equal rights for LGBT, then it's a valid act of quasi civil disobedience and he was wise in selecting it because obviously he is where he is now.
He should be applauded. Of course, reciting the pledge is a patriotic act, but only in a superficial way. Fulfilling the meaning of the pledge in our actions is much more important to the purpose of our country, and in that sense, people often seem to have forgotten what the pledge really means.
It's not unpatriotic to use your rights to make a point, even if it offends some people's sensibilities about established customs. In fact, the opposite is true. It's unpatriotic in the United States, a country founded in the ideas of liberty, to sit around with nothing useful to say when other people's rights are on the chopping block.