i tried Cosmic Fantasy 2 with Daemon Tools Lite 4.30.3 and it mounted fine and ran on MagicEngine afterwards
so i guess something must be wrong with those files you have

i must admit those 'decompress.bat' files are quite bad -
they do check CRCs for included files, and hence their presence but this information rush very fast on screen
there should have been pause after completion and an option to specify target path

so you could try to redownload this CD
or delete *.bin, navigate to source directory from command prompt
(or you could use FAR manager - it helps a lot for such tasks and it's free)
and execute 'decompress.bat' again
it should display 'everything is fine' in the end, like this:

if it says 'error verifying .bin!!!' instead - some of files are missing then

and also there should be .cue present in the same directory - it isn't checked from .bat

so i hope this will help,
i won't be around for some time,
so if there still are some difficulties i hope somebody else will be able to assist you

You're actually the person who led me to this site via your torrents on pirate bay. I was pursuing Cosmic Fantasy 2 for the Turbo Grafx and a way to play it. You helped me to finally after over 12 years be able to play it again. For that, I thank you. ^_^

...however, I'm still trying to figure out how to get it to work properly. I managed to get Cosmic Fantasy to work, or rather, for daemon to recognize it and load it as a CD, but I have been unable to do it with Cosmic Fantasy 2. Each time it tells me it can't access it or something...

Either way, thanks! ^_^

.dat is there to provide an convenient way for comparison of CDs among people
for example you can take image from CD by yourself and make sure it matches to other dumps
for emulation per se it's unnecessary

to run an game on emulator you'd need either CD or CD image
in case of CD it's straightforward, for image ther's usually alson an cuesheet that describes it's content