I'll be honest. The first time I saw one of these cartridges, I thought they were pirates. However, the chips inside are have official Nintendo part numbers and have "(C) NINTENDO" on them, so there's no other conclusion to make except that these are official Nintendo-produced products.
The cartridges themselves are really nothing special; it's their origin that's the real question. The art used is always from the true Famicom version of the game. The plastic is a lighter gray than normal NES carts, and "Asian Version" is printed on the bottom of the label in English and Chinese. Some carts have the European circular version of the "Nintendo Seal of Quality" on them, and some have no seal at all.
Where did these things come from? My best guess is places like Hong Kong, Taiwan, and southeast Asia. Game Boy carts of a similar nature have been spotted in K-Marts here in the US, but these Asian Versions are a different story altogether. Even stranger is the way Nintendo uses the American names of games in Asian Version carts. Kung Fu was called Spartan X in Japan, but was renamed to Kung Fu for everyplace outside of Japan, including the US and the rest of Asia.
Still, there are far more questions than answers about these carts, and it's difficult for an American collector to come up with much information about these. Exactly how many titles were "Asian Version"ed is a mystery, but it appears that most of Nintendo's early catalog was released like this. Perhaps Nintendo gave up on the rest of Asia after pirate cartridges started to be released en masse...? As with too many of the other things I showcase on my page, there's not a lot more to be done than speculate on origins.