You're right. Part of Kansas City is in Kansas, and the other part is in Missouri.
However.................the part of Kansas City that the Chiefs claim as their home is the stadium located in Kansas City Missouri, not the part located in Kansas.
Here, maybe this will help you out...................
Kansas City Chiefs - Wikipedia
The
Kansas City Chiefs are a professional
American football team based in
Kansas City, Missouri, and current
Super Bowl champions. The Chiefs compete in the
National Football League (NFL) as a member club of the league's
American Football Conference (AFC)
West division. The team was founded in 1960 as the
Dallas Texans by businessman
Lamar Hunt and was a charter member of the
American Football League (AFL). (It is not associated with the
NFL Dallas Texans.) In 1963, the team
moved to Kansas City and assumed its current name.
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But, if you choose not to believe it, you can Google it for yourself by asking where are the Kansas City Chiefs based.