Ok, this one seems to work a lot better, when I first launched it it did not work at all. However after going into the System Preferences and removing the BTT entry from the Accessibility section and re-adding it the application would launch and work smoothly, however the application was previously approved and had a check next to it. (Removing and re-adding the application here was something that I had tried with at least one of the earlier builds - I believe I tried it on 2.514)
Interestingly clicking the check mark for BTT (and some other apps) would not toggle the checkbox at all, after attempting to toggle it twice the application would then continue to launch, however it would not accept any keyboard shortcut triggers (it would also say "There was an issue restarting BetterTouchTool. Please do it manually" upon launching). Even when it is working it gives this same error message when you attempt to "restart" it from the dropdown menu.
In conclusion - the new build works for me if you remove BetterTouchTool from the System Preferences -> Security and Privacy -> Accessibility and re-add it! And it seems like there might be some bugs in System Preferences / access permissions on the MacOS side.