It actually is from the Shell presidents game, in a round about way, the set of bronze colored medals with presidents was one of the prizes.
There have been a lot of different sets of these made over the years. The Shell set is probably the most well known. The US mint has even made one for each president but they are a bit larger. Just for fun. Not sure who made these but not the US mint.
This token was made by the Scovill Manufacturing Company of Waterbury, Connecticut during the early 20th century. The Scovill Company was established in 1802 as a button manufacturer and is still in business today. Scovill was an early industrial American innovator, adapting armory manufacturing processes to mass-produce a variety of consumer goods. Obverse: Bust of John Adams facing right. Legend: 2ND PRESIDENT, U.S.A./ 1797-1801/ JOHN ADAMS. Reverse: Legend reads: "SON OF LIBERTY"/ "COLOSSUS OF INDEPENDENCE"/ MINISTER TO ENGLAND VICE PRESIDENT TWO TERMS CREATED U.S. NAVY ON ACCOUNT OF EUROPEAN WAR CLOUD FIRST PRESIDENT TO OCCUPY WHITE HOUSE.
The original funerary tokens may be valuable. An interesting side note from reading about early numismatics in the US - George Washington buttons, tokens, and medals were the *big* item in the early 19th century. If memory serves, a collection of Washington tokens formed the basis of the Smithsonian's collection.