So I did a bit of digging around on the Japanese cards because the artwork on those look AMAZING.
It seems that the artwork on those cards are from an illustrated guide called <<ポケットモンスター全わざ大図鑑>> (Pokemon All-Purpose Illustation Book). It was released in September 1997 and it details the original 165 moves in the Pokemon Red/Green games. In terms of content, you will find illustrations of the moves along with things like the move type, PP, power, accuracy, effect, a list of Pokemon that can learn the move, etc. The book itself was published by <<ティーツー出版>> (T2 Publishing) which was a fairly well-known company in Japan for game guides and magazines at the time. They have since shut down.
As far as the illustrations are concerned, they were done by an individual named <<成田保宏>> (Yasuhiro Narita). I searched around a little because that wasn’t a name I recognized, but now I’m confident that Narita was simply a staff illustrator contracted by T2 Publishing; he is not directly associated with the Pokemon franchise. With all that said, it’s still a bit of a question mark as to how these illustrations ended up on the back of stickers/cards. My guess is that T2 made some agreement with a 3rd party to have these distrbuted via vending machines. But really, your guess is as good as mine!
@cracker , there seems to be several listings of this item on YAJ and other JP sites if you’re still interested in hunting one down (they are very reasonably priced).
Front:
Spine:
Back:
One of the pages:
(Images are from YAJ)