No, they'd fit in just fine.  I know I didn't mention any female gladiators, but the arena is owned by a woman.  In fantasy settings I prefer to have cultures be more progressive regarding gender than they were in real life, because it makes for a greater range of characters.  

That said, female gladiators are rarer than males.  Because female slaves have even more barbaric uses.  Most women gladiators are actually willing volunteers.  

By the by, I don't know if everyone missed the fact that not all gladiators are slaves, but some of them are just athletes seeking a very risky glory.  
Also note that not all slaves come from conquest.  Many are born into it, or else sold into the Anaxan market by their own countrymen.  You can also be enslaved as punishment for a crime.  

I hope nobody is upset if I take the basic premise of your character's culture and sort of run with it.