These other 'Note 3' devices have packaging that is also laid out to look like Samsung packaging as well but without the Samsung name printed on either the phone or packaging.
Many of them do actually have the Samsung logo on the packaging, the phone and a pretty close approximation to a Samsung internal label.
Netmantis, you aren't flashing a ROM 'over' an existing ROM, you're flashing a ROM 'instead of' the existing one. If the hardware will run the custom ROM, it will work regardless of what ROM is currently in it. (I've used the 9005 ROM in my 900A - totally different market, but similar enough hardware to work.)
I wouldn't even attempt it, though, unless I had the stock Chinese ROM to flash in case it didn't work. If the custom (or even stock Samsung for another market) ROM doesn't cause any damage, at least you'll be able to reflash the original Chinese ROM.
Be prepared, after flashing a ROM. Boot into recovery and do a factory reset. Then do a normal boot and be prepared to wait up to 15 minutes for the ROM to rebuild the system before you're at a homescreen.
What you were told, what Kies sees and what's in the phone may all be different. If the hardware in the Chinese version is different enough, the 9005 ROM won't work (and neither will any other Note 3 ROM).