Here's why:
* Bottomless Trap Hole activates when an opponent Special Summons a monster.
* Red-Eyes Darkness Metal Dragon is Special Summoned by its own effect, not by the opponent.
Because Red-Eyes Darkness Metal Dragon's Special Summon is triggered by its own effect and not by the opponent, Bottomless Trap Hole will not activate.
Important Note: While Bottomless Trap Hole won't stop Red-Eyes Darkness Metal Dragon's Special Summon, it can still be destroyed by other card effects that target monsters, such as "Torrential Tribute" or "Solemn Judgment."