" The referee of the match" alternative?
We have "match" in the incubator. Did you try it?
"The referee of the contest"? Also you need to have "umpire" as a translation of διαιτητής (primarily tennis, but also cricket and baseball).
For "contest", you'd use "διαγωνισμός" more often. You are correct in pointing out that "διαιτητής" is also the word for "umpire".
I got thumbs down for 'the umpire of the match'? (reported)
Yes, sorry we had a technical error. It's ok now. Thank you.
"The game referee" sounded like more natural English to me. Not accepted.
It's simply not an English expression. An Ngram test did not show a single reference to it.