Since Mac App Store apps are sandboxed by Apple there are some API:s that can't be used. All app developers face this issue and many apps are different in the Mac App Store because of this.
The free version of DaVinci Resolve can be downloaded directly from
https://www.blackmagicdesign.com/support. If you need the Studio version you have to buy either an activation key or a USB dongle (and download the Studio version from the same link). You can only buy from retailers, not from BMD directly.
Since old dongles work as well, you can also get cheap dongles on Ebay.