The use of the word to refer to a political "party" predates the use of the word to refer to a group of people gathered together for other reasons.

"Party" has the same root as the word "part," i.e., it means one of several divisions. A "party" came to mean a political division around the year 1300 (it comes from Middle English). Later, "party" came to refer to any group of people, and not just a political group, although this kind of "party" was distinctly defined, i.e., you could have a "hunting party," "dinner party," or a "search party." Finally, the word took on the connotation of a party specifically gathered for the purpose of social entertainment.