No, it's not necessary to buy the application again because apps purchased from the Play Store don't work like that. It doesn't matter if you replaced the phone and factory reset it. As long as you add the email that was used to purchase the application, the Soundabout Pro can be installed again forever or until you lose the account.
Kindly configure your phone again, attach the account using Settings > Accounts > Google, then use Play Store and the software will be available for installation.
