This claim is false and satire.
The source itself, The Dunning-Kruger Times, says that their "a subsidiary of the 'America's Last Line of Defense' network of parody, satire, tomfoolery, or as Snopes called it before they lost their war on satire: Junk News" (from their 'About Us' section on their website). They also wrote that "satire is the use of humor, irony, exaggeration, or ridicule to expose or criticize people's stupidity or vices, particularly in the context of contemporary politics and other topical issues." In this case, they used satire to talk about how huge Taylor Swift's and Travis Kelce's relationship is right now in pop culture.
In terms of the claim, I looked up the claim that the Kansas City Chiefs will not re-sign him, and I found no sources that support this claim, but a source called Lead Stories, which also fact-checked this claim, and also found no evidence that the claim is correct.
https://leadstories.com/hoax-alert/2024/02/fact-check-kansas-city-chiefs-wont-be-re-signing-travis-kelce-weve-had-it-with-the-side-show.html