This card's extra drawing effect can replenish hand advantage more reliably than other Gladiator Beast monsters (such as "Gladiator Beast Torax") and the extra drawing effect can help in the use of the effect of "Gladiator Beast Heraklinos", which requires discards. It's similarly handy for "Parry" and "Disarm".
Since the drawing effect requires the player to destroy a monster, "Trojan Gladiator Beast" can help to send a low attack monster to the opponent's side of the field with the added bonus of drawing one card.
Since this card's unique effect can trigger multiple times from destroying monsters by battle, "Gladiator Naumachia" can be useful in forcing the opponent to attack this monster.
Special Summon this card and "Test Tiger" with the effect of "Rescue Cat", then use the effect of "Test Tiger" to tag this card out for whatever Gladiator Beast would be most beneficial at the moment.
Alternatively, Special Summon two copies of this card with "Rescue Cat", attack with both, and then tag them out. This is more risky, as they might be destroyed, but more rewarding as you can tag out for two Gladiator Beast monsters instead of one.