The Mac Operating system sometimes blocks unsigned apps from playing. Please use either the itch.io launcher or adjust your privacy & security settings.
You can also download the demo on Steam, which also works on Mac without any adjustment to privacy & security settings:
https://store.steampowered.com/app/2313010/Date_Time_Melissa_Morris_Anna/
First, run the demo and receive the error again. Then, go to your settings and under "Privacy & Security" there should be something like 'Date Time Demo' was blocked to protect your Mac. There should be a button next to it that says 'Open Anyway' and Mac should run the app from now on without any issues.
More info: https://support.apple.com/en-us/102445
However, if you are still unsure about running the individual app file, you can always play the game through Steam or Itch.io Launcher, and Mac will not block those connections.
Apple will always block apps from developers they do not have in their database. A lot of smaller game creators don't really upload their stuff to Apple's app stores, so that's probably why Apple blocks a lot of different games you are trying to play.
I think Mac only keeps your last 'block app' in memory for a short period of time, so open the app again and then immediately go to the settings to check it.
If that doesn't work, it could be a myriad of things, including if you have admin access to the Mac or some other issue that I'm not aware of.
Again, if the problem persists, you can always use Steam or the Itch.io Game Launcher.
Mac will usually allow opening of games downloaded from either of them.
