Per the OED, the word staple comes to us from the Old French estaple meaning an emporium or market place. It originally (in the 1400s) meant an English town, the merchants of which had a royal charter to deal in certain goods. These goods or staple-wares came to be called staples about 200 years later, and that word designated the principal commercial product of the district surrounding the staple (the town). In modern parlance, staple acquired the meaning of the basic food stuff on which a community relied. Ask a browser to search for the words "staple" and "Ireland," and you shouldn't be surprised at the number of results containing the word potato.
The Corpus of Contemporary American English tells us that the two most popular locutions for the scope of the word staple is "staple of" (as in the OP's question) and "staple in." The following table tells how many different words were found to follow these phrases, and how many of those were unique. The large number of unique occurrences tells us that people are comfortable with using the word staple beyond food stuffs to designate basic items in just about any category, from "staples of science" to "staples of sitcoms" and from "staples in classrooms" to "staples in books."
phrase occurrences singletons
------ ----------- ----------
staple of the 158 142
staple of 366 302
staple in the 46 38
staple in 107 99
(The "staple of" list excludes "staple of the" examples; the "staple in" list excludes the "staple in" examples.)
The word thus has the attributive meaning of basic, important, and standard, so a staple anything is something that is customarily found in some situation and that should be expected in that situation. So the article quoted by the OP says that for the last 150 years, hosts have given their party guests bags of goodies containing the game, so it's become a standard element of the gift.
It may help to consult answers that have appeared before in response to questions about media staple (a common story appearing in the news), music composers as staples (about standard classical music), the attributive use of textbook as a synonym, not to mention dietary references
Addendum: A kind commenter has asked me to explain what "party-favor bags" are, in case that this reference was part (or all) of the confusion. A party favor bag, also called a goody bag, is a small container with gifts for the guests at a party. These gifts may match the theme of the party, should the hosts have designed their party around a theme. Naturally Amazon has a wide selection, which you may peruse by following the link.