Similar situation applies to Turkey, it's defined as being in "Eurasia", which is defined in the 6-continent Eurasia model, generally preferred by the scientific community. As it spans 2 continents europe and asia are split by the Ural mountains, which run through Russia, so technically part of Russia is in Europe. Countries like Israel also manage to get into European events such as the Eurovision song contest and I believe the European football.
I think Moscow is technically in Europe, so that's why it's allowed the final.
It's more to do with which body they are affiliated to. Israel is in the Eurovision Song Contest because they're members of the European Broadcasting Union. Russia, Israel and Turkey for that matter, are affiliated to UEFA.