The ② effect:
It can't be activated unless there is a "Gladiator Beast" monster in your Deck.
It can activate and resolve while "Skill Drain" is applying (without being negated).
It can be negated by "Royal Oppression" (If it is, this card remains in the Deck (it is not destroyed)).
"Battling" requires this card to be involved in Damage Calculation (If this card's attack is negated, the ② effect can't activate).
If multiple "Gladiator Beast" effects are activated at the end of the Battle Phase, they don’t go on the same Chain (they each activate, one after another, each on their own Chain). Vs "Rivalry of Warlords"/"Gozen Match":
If you have a Gladiator Beast of the same Type/Attribute in your Deck, you can activate the ② effect. If you do, you can Summon any Gladiator Beast of any Attribute.