IDK, it seems to fit with the definition to me:

https://dictionary.cambridge.org/dictionary/english/politics

> the activities of ... people who try to influence the way a country is governed

Britannica says politics is "the opinions that someone has about what should be done."

"playing politics" itself apparently also has its own definition: https://www.merriam-webster.com/dictionary/play%20politics

But I moreso meant the plain politics definition.