Well as an exercise, I extracted the Center Court 2 files on my PC using WinRAR, copied them to my FAT SD card, ran from there and just fine. Then I copied this folder to my Amiga HD and it again ran fine. So whatever was happening to this guy, was his own issue, maybe/probably having to do with his choice of file extractor? No idea.
I find that the "unpack only in Amiga" camp can be over-zealous about the issue and it doesn't always hold true. There are cases where it is (like with weird filenames as I mentioned before) but usually it's fine.
Then again, Amiga CDs conform to CD filesystem standards, so they shouldn't have Amiga-specific attributes on them. Here is a screenshot showing attributes for different files on a Microcosm CD I have, and despite some being data and one being an exe, they all have the same flags on.
So I again think copying from a PC with a CD drive would work just fine. And if you are SUPER ANAL about it, mount the disk on a PC using WinUAE and then copy from within the Amiga environment into an LHA file or whatever. You still don't need an A1200 with a CD drive.
+1 for using ZIP to compress Amiga files being a stupid idea, LHA all the way.