If your store is over head count, has someone on the bench , or wants to switch a TL to that work center, or has a transfer coming in, then no, they don't have to interview you and can turn down your application.
Stores are required to have TMS on the bench as well. So it's unlikely they would have to even interview unless they have other positions in mind for the bench TL. With the start of the 4th quarter, stores over head count are trying to get rid of their TLs.
Just shine and don't give them any reason not to choose you next time. Remain calm and level headed. They don't want a TL who is going to cause an uproar when they don't get what they want. It causes tension and gives the impression of immaturity and a lack of stability.
Also, interviews are not the final say. I've had people flunk interviews but had a feeling they'd be a great asset and it's worked out. The same vice versa. If they don't think you're the right fit then an interview won't change anything.