So I was browsing eBay for promotional variants of the Game & Watch and found this listing:

www.ebay.com/itm/Nintendo-Game-Watch-OCT...n-Japan/303173738397

I took a look at it after noticing it had an unusual print on the side. As it turns out it was a previously undocumented CGL (CGL being the UK distributor of the Game & Watch) promotional variant of the game Octopus. Hopefully more information about this can be found soon.

Edit: Turns out I'm an idiot and didn't realize that CGL just put that logo on all the Game & Watches that they made.

Archive.org listing:
web.archive.org/web/20190613194015/https...n-Japan/303173738397