I was searching through the US Patent and Trademark Of)fice database for random companies (you can search it here: tmsearch.uspto.gov/bin/gate.exe?f=tess&state=4804:ox2yk6.1.1 ) and found a trademark registered by Nintendo with the following information:

Word Mark LIMITED EDITION ARABIANS INC.
Goods and Services (ABANDONED) IC 014. US 028. G & S: WATCHES, CLOCKS. FIRST USE: 19800422. FIRST USE IN COMMERCE: 19800422

(ABANDONED) IC 028. US 022. G & S: TOYS, PLAYTHINGS AND GAMES. FIRST USE: 19800422. FIRST USE IN COMMERCE: 19800422

(ABANDONED) IC 042. US 100 100. G & S: IN THE BUSNESS OF BREEDING ARABIAN HORSES IN THE BUSINESS OF BREEDING ARABIAN HORSES. FIRST USE: 19810600. FIRST USE IN COMMERCE: 19810600
Mark Drawing Code (3) DESIGN PLUS WORDS, LETTERS, AND/OR NUMBERS
Serial Number 73386263
Filing Date September 17, 1982
Current Basis 1A
Original Filing Basis 1A
Owner (APPLICANT) LIMITED EDITION ARABIANS, INC. NINTENDO CO., LTD. LIMITED EDITION ARABIANS, INC. CORPORATION KENTUCKY 41 LOGAN RUN BURLINGTON KENTUCKY 41005
Type of Mark TRADEMARK. SERVICE MARK
Register PRINCIPAL
Live/Dead Indicator DEAD
Abandonment Date December 30, 1983

According to this database, it was first used for a commercial product on April 22nd, 1980. This is also the same date mentioned as the date of first use for a commercial product (in the US obviously) for the Game & Watch trademark. Not to mention that in the Good & Services section, the listing mentions watches, clocks, toys, and games.

It's clear that this is in some way related to the Game & Watch in the US; the question at hand is how?