Travel for Student holding L2 dependent Visa

My daughter (who holds an L2 visa valid until Sept 2022 ) is traveling to India on July 28th to attend an F1 visa interview scheduled on August, 3rd. In case if due to any reason F1 visa is not approved can she still travel back ( on her L2 visa ) to the United States before August, 10th to attend the admitted college, as the travel ban is applied only for non-immigrants who are physically present in India for 14days or more?

Thank you!

Your daughter may travel back to the US using a valid unexpired L2 visa and I797. Make sure the passport is valid beyond 6 months from the date of entry.
If in case the passport expires before the expiry of I797, she will get her I94 issued only till the passport expiry date at the port of entry. If this happens, she will need to visit border CBP ( most people visit Mexico border) to renew her I94 before it expires so that it can be updated to match her L2 I797.

Do you mean during president proclamation travel ban from india this situation is valid?

Yes if your daughter qualifies for travel exception.