Indeed, a non-transitive election like that means that there is no Condorcet winner. Some voting methods (including first past the post) are guaranteed to select a Condorcet winner if one exists, but when one doesn’t exist (if A>B>C>A), various voting methods will result in various winners.

I love reading about the theory behind voting methods, but one common criticism is that these edge cases are rare and thus a pure theoretical approach isn’t sufficient for getting a “desirable” (however you define that) outcome.

https://en.wikipedia.org/wiki/Condorcet_method