You may encounter problems that you fail to install Bandizip or to run it after the installation. This isn’t just about Bandizip; the same problems are reported in other apps on the App Store like the link below.
Some Mac App Store Apps 'Damaged' Due to Expired Security CertificateIt is assumed that the problems have occurred since the introduction of Gatekeeper, macOS’s new security system. Until recently, there have been sporadic reports on failure to install apps or to run them.
There are some of the possible ways to solve the problem as follows:
How to clear the cache: Clear Mac App Store Temp Cache to Fix Some Download Issues
If all of them don’t work, you need to contact Apple Support to solve the problem.