Someone else asked me to look into this.
After looking at the program's PE Header, I found the problem. The 'Major Operating System Version' and 'Major Subsystem Version' numbers were set to 6. Those parameters specify the MINIMUM Windows version that is required. For XP to run the Raidy .exe files, those numbers should be set to version 4. The Windows program loader code doesn't give specific error messages, so that's why you just get the generic 'Not a valid Win32 Application' error message.
In other words, the IDIOT who compiled the program didn't set the minimum OS version numbers correctly; The linker's OS version parameter needs to be changed.
If you don't want to wait for a patch, then get a hex editor program (a free one like HxD) and make these changes.
For both Raidy3.exe and Raidy3_Windowed.exe files:
1) At file offset 158, change the '06' to ''04'
2) At file offset 160, change the '06' to '04'
I won't upload files because it is illegal to upload (i.e. share) copyrighted files.
Whoever reads this message, please pass this information around the internet so that other people won't have to wait a ridiculous amount of time for a patch. You can also pass this information on the JAST for me, because I won't bother. (I'll probably start chastising them about their bloated, slow programming --their use of complete garbage like LUA is a dead giveaway.)