I would suggest contacting your Red Gate sales representative to see if they can set you up with a 'restore only' license, or you could just write directly to sales@red-gate.com to explain your needs. In the meantime, you could use a trial license on the other server to test your restores.
Another option, space and time permitting, is to convert the SQL Backup backup file to a native SQL Server backup file using the SQL Backup conversion utilities (no license required), and restore from the native backup file.
Another option, space and time permitting, is to convert the SQL Backup backup file to a native SQL Server backup file using the SQL Backup conversion utilities (no license required), and restore from the native backup file.