The ending of The Hunger Games explained
Because Coin was evidently one for sinister pageantry, she decided to make Snow's execution public. So, Katniss, armed with her bow, was all set to carry out Snow's death sentence in front of the whole of Panem. But with Snow's words about Coin in mind, and the knowledge that the incoming president planned to be just as cruel as the last, she assassinated Coin instead, with the intention to take her nightlock suicide pill soon after. Katniss knew her reasons for killing Coin would be unknown to most of the public and that she'd be tried as a traitor, but she was willing to trade her own life to ensure the vicious Hunger Games never happened again.
Her self-demise attempt was thwarted by Peeta, who'd started to decipher "real" from "not real" when it came to their shared history, and she was instead jailed for the murder of Coin. In the book, she was later acquitted on account of insanity. In the movie, new President Paylor, formerly a central commander of the Resistance, quietly pardoned her for the crime. Meanwhile, Snow was killed in the riotous melee that ensued after Katniss' assassination of Coin.
Did Snow play Katniss one last time? Yes. But there was also some of the same willful defiance of the Games contained in her action, too. Just like the first time those nightlock berries came into play, when she and Peeta held them up together to deny the Capitol a victor in the first round, she wasn't going to submit herself to the spectacle of such a public trial and execution as the ravenous public would invariably want. Luckily, she still managed to escape the media spectacle thanks to the mercy of the incoming administration.