Under Archetypes for Arcane, Expert, and Martial you (such&such) Armor Proficency in your REGIONAL armor as seen in table 2-27. MOST backgrounds give you some type of armor to start out with in it's items list. In the "Former Gladiator" background that armor happens to be Gladiatorial Armor.
However the Background also has the requirement to be from Almeric, Coryani Empire, or Hinterlands. None of those Nations have Gladiatorial Armor as choice on table 2-27.
What that means for the player is that your character has been training and fighting in their armor for a good long time. Long enough to retire/win their freedom. They get to walk away with some silver, three gladiatorial weapons, travelers kit, and the Gladiatorial Armor on their back (they don't even get common garb). Because, the armor is not listed on table 2-7 they can't even use the armor they trained in.
I can think of three errata fixes.
1. Add Gladiatorial Armor to those three Nations. (This is an easy rules fix but does not fit the flavor text or I think the intent of Gladiatorial armor)
2. Add the Talent - Armor Proficiency: Gladiatorial Armor to the Background Former Gladiator. (This one makes the most sense but some might see it unfair because it gives the Gladiator an ungodly amount of talents as they have separate Weapon Training Talents in all the Gladiator weapons.)
3. Change the rules for the item itself by adding some sort of statement.
That Gladiator Armor is considered to be any type of light Armor but one must specify the type of base armor. (I think this one fits well with the flavor text of the armor but I think this one would definitely make Pedro cringe
)