Screen Shot 2019-05-30 at 10.59.18 AM.png
The manual install ZIP file contains both Windows and Mac versions, so Mac users will want to simply ignore all the .exe and .dll files.
Fortunately, the process is fairly simple for Mac, albeit slightly confusing because what you want here are the two that are both named "RaceRender 3"... One is a folder containing templates and styles, which you should drag into your own user "Documents" folder. The other is the actual application (has a .app extension but you usually wont see that), and if you drag that into your computer's main "Applications" folder, it will then appear in Launchpad. Alternatively, you can put it on your desktop or wherever else and launch it directly from there.
As for the Mac installer... yeah, that has unfortunately become increasingly problematic and Apple has since abandoned the tool that creates it, so we'll probably replace it at some point. It does still work in many cases, but seems to have the problem happen most when applying an update on top of an existing installation, although trying it repeatedly sometimes works (same for rebooting the computer and trying again). It acts a bit like some sort of race condition that we aren't given any control over. I share your frustrations. We may end up just going to the .dmg approach that so many other Mac apps use, although that's really just a manual install process in disguise and has its own drawbacks.