Translation:The 81st athlete is not running, but walking.
While it's not strictly incorrect to say "he is" here, it sounds kind of weird; usually such a construction is used to put lots of emphasis on the verb in a way that only context - which is missing here - renders logical, e.g. "The eight-first athlete [sprained his ankle and therefore] is not running, but he is walking [, so he must not be hurt too badly]."
If that's not what they're trying to get across, then just "The eighty-first athlete is not running, but walking." should be accepted. If that is what they mean, then they should make that more clear.
Omitting "he is" from the translation would be the solution, as in the context you described ("but he is walking"), Hungarian would use the conjunction "de" instead: "A sportoló nem fut, de sétál."
(Or for extra emphasis you could say "A sportoló nem fut, de sétálni sétál." A pretty weird structure, I know. It means something along the lines of "He is not running. But walking -- he is doing that.")
Is the difference between "nyolcvanegyedik" and "nyolcvannegyedik" actually audible in everyday spoken language?
"Nyolcvannegyedik" is pronounced with a long or stressed n, while "nyolcvanegyedik" (surprisingly) with a long gy. (It's pronounced so in the word "egyet" as well. A common mistake among children is to spell this word as *eggyet)