Generally you can tell the kind of file by its file extension like in this case, .exe. Some are obvious like .txt (text) and some are not so obvious. There are web sites specifically for looking up file extensions like FileInfo.com. And there are local ways too, for example, seeing what the finder thinks it should open for a file via Get Info. It's not always correct (and sometimes gets confused) but it may work. There are other ways as well using terminal which I won't go into here.
Stuff written it flash is something like pdf, i.e., platform independent. Generally any flash player can play flash as most pdf viewers can read basic pdf (there's some pdf files Adobe Reader can handle that Preview can't).
As I said for your situation above, that .exe file may be a self-extracting file which produces the flash game which potentially you could run. But since you can't directly run the .exe it's academic. .exe is an example of a executable file. Executable are not platform independent because they have a file format and machine code dependent upon the OS in which they run.