Translation:His failure is a consequence of my success.
'Outcome', 'result' and, 'consequence' are similar but different in meaning. An outcome is just the final state after an event or process. It doesn't necessarily imply that causation is involved. It could be luck. A result is normally something that very directly follows from something else (eg the result of adding two numbers). A consequence is something caused by a prior event or process. It would not normally be used for something completely determined by the prior event.
Almost the same, but in English words with similar meanings are often used in totally different ways.
It's true that "outcome" is often a synonym of "result", but for me it wouldn't work here. From Longman Dictionary:
"the final result of a meeting, discussion, war, etc – used especially when no one knows what it will be until it actually happens
It was impossible to predict the outcome of the election.
People who had heard the evidence at the trial were surprised at the outcome
I think that it might be because we wouldn't say that something "was the outcome of my success", but that "the outcome" was that something happened.
But to me, not to him. His failure might have been the consequence of my success, but it wasn't an outcome, or even a result. Talking of a race, for example, we don't say that the result of A winning was B losing. Perhaps:
"I was very successful on the course and the unexpected outcome was that I was offered a job as a teacher"