I can open the game from the zipped folder and play fine (but it doesn't save)
You should not do this. The game can't save anything and you will ultimately have lots of corruption and problems. Always unzip it.
but when i extract and open the game from the there, the screen for Mythruna pops up really fast and then vanishes, and then nothing happens.
Acer Laptop with Windows 7
Which "screen for mythruna"? Where did you unzip it?
It could be a file permission problem, I guess... but I'd need to know which screen it failed on and whether it was able to extract its DLLs etc. into the directory you unzipped it into.