Of the hundreds of games I've seen here, only this one seems to have an Exe installation. I don't understand why such a preference was made. Having the game files openly in Zip or RAR without setup helps to make a safer installation when scanning for viruses.
It used to be a lot more common, to the point that you basically never them in any other form. Many people didn't realise you could rename it from a .exe to a .zip/.rar instead and extract with whatever archiving software you had installed.
If I had to guess, I'd say it's part of the anti-cheat measures.
Nope.
Games from older versions of RPGMaker (such as the one for this game, RPGMakerVX Ace) typically were distributed in a self-extracting archive, and often two different versions of the same game could be found - RTP version and non-RTP version.
The RTP version meant you didn't have to download and install the necessary free runtime files from RPGMaker's website for the specific iteration of RPGMaker that a game was made in.
Every time I've tried to use the RPGMaker cheat engine it just deletes the game while trying to open it, creating a backup version of the game with all the same saves. Never had another game do that, never had another game have an exe installation
That has nothing to do with the download being a self-extracting archive.
In fact, I've never heard of using Cheat Engine with any game resulting in the game being deleted and a backup made, and that's over a period of roughly a decade.