I am not sure about the other specialized programs in NYU (and other admitted applicants), but I think that generally NYU will look at your profile and experience, aside from the usual law school rank and other criteria.
Congratulations for your admission to NYU. I have applied the corporate program and I do worry that the competition in this program is much more intense than in the general LLM.
I think the only difference is that experience will somehow matter in specialized programs, although other admitted students may correct me on this.
Don't lose hope. I heard that the school is still rolling out admissions until late March!! Wish you all the best in your application!!