Wow, great description you've got there. You just called it a horseman, you really needed Latin for that to sound intelligent.
From wiki
A Hoplomachus (pl. hoplomachi) (Greek: ὁπλομάχος) (hoplon meaning "shield" in Greek) was a type of gladiator in ancient Rome, armed to resemble a Greek hoplite (soldier with heavy armor and helmet, a round shield, a spear and a sword). The hoplomachus would wear a bronze helmet, a manica on his right arm, loincloth (subligaculum), heavy padding on his legs, and a pair of high greaves reaching to mid-thigh. His weapons were the spear and a short sword.
Eques, indeed is a horse in latin, but that is just one meaning. They would open up the gladiator fights on horseback, however you wouldn't know that, because the english wikipedia doesn't contain that information. The German wiki does and I will use the google translator for you, because I am not willing to translate myself.
The equites opened its struggle with the gladiatorial games. They were with a brimmed helmet with visor, a flat round shield, a lance and a short sword gladius armed. Were in contrast to all other categories of gladiators, who dressed only in a loincloth subligaculum, they wore tunics. They began to fight on horseback, dismounted and then put him away with their swords. In pictorial representations, they are mostly represented in the final phase of the struggle, that is descended from a horse and on foot with swords fighting.
In retrospec you should have remained silent, because it doesn't make you look very 'intelligent' if you argue with nameroots when there is more to the word, especially since Hoplomachus doesn't have anything to do with 'Horse'.
Although I cannot comprehend how it is relevant in NAMING a build, a class so to speak if that perticular type was used in an military army. However bringing up that argument will net you another slap to your face:
There was a gladiator army, not for rome, but against rome. You can even watch a show: Spartacus: Blood and Sand + sequels. In case you didn't know it is a representation of what information we have of that era, and we know, that those gladiators formed an army by giving training to slaves as they received as gladiators. So gladiators train more gladiators until they reach army size.
Of course they also trained archers and such, but their frontline consisted of gladiators.
