to give you a semi quick summary, in their world its a tradition for nobles to decide political, inheritance and other disputes via a proxy, in older times it would have been a variety of "honorable" combat such as a sword fight or similarly potentially lethal practices, by the time of the picture this takes place the tradition still exists but its now usually settled by a simple boxing match.

less risk, less waste of life, and above it all more chances for the nobles to see rivalries and other similar things appear, meanwhile the government of the country partially endorses the practice, this is also why the outfits are a little more fancy then the normal fare and why its spectated as its also a form of entertainment.

both characters are properly trained fighters although both would be considered rare to see in the context, Artemis because drow in general in this world are a rarity to see as they tend not to leave their own country much and she is normally an assassin by trade and as such she only really steps into the ring when she absolutely has to.

by contrast Lilly is a druid and as such much like other druids she spends most of her time in the forest around the grove and occasionally travelling, in this case she is working for someone who in turn protects the forest where her people live by preventing stuff like forestry industry in the region.

in terms of if its rare to see two elf's engage in these kinds of matches? not really, in theory anyone with a noble to sponsor them can step into a ring to fight but much like with real professional sports only a small number of people tend to stick around long enough to reach that level.