To me, the mere word "successful" doesn't completely spell that out. "Successful", in this context, could be interpreted to mean that an offer was made and accepted. Also, "Successful" may be interpreted to mean an offer of acceptance along with a certain level of financial support.
Clearly, Columbia and Michigan spelled it out much more clearly. They did not use phrases like "if your app is 'successful'". Instead, they simply state that if an offer of admission is made to the applicant, the applicant is bound to matriculate at the law school and withdraw all other applications. No ambiguous use of the term "successful application".