This is correct.
We wouldn't normally say "He COMES in eighth" unless it was followed by "every time" or some other qualifier.
Normally, we would say, "He CAME in eighth" or "He came in AT eighth place." (How do we know what place he achieved until the contest is over?) If it is present tense, we would say, "He IS in eighth place."
We might also say, "He IS COMING in eighth."
Yes the tense is incorrect in the English translation. You could use ' What was his final position? He came in Eighth place', presumably as one cannot come in any place until the event is complete. Even the suggested 'He comes in at Eighth place', would be used possibly only when someone is just completing the act. Who knows? :D
Actually, I'm thinking of a marathon, for example, which might have many competitors, so the event might be ongoing (there is still a 9th, 10th, etc. runner yet to come in). This is how Jeanbean42574's example about him being in 8th place makes sense to me. I don't think the tense is incorrect in English; I think that we use tense differently around simple and progressive present tense. I definitely don't fully have my head around it, but I think that might be what's going on here.