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Game mechanics refer to any action that automatically happens due to the interior workings of the game's rules. Cards destroyed or otherwise moved by game mechanics are not considered to have been moved by an effect.
Field Spell Cards
Each player only has a single Field Zone, so can only control 1 Field Spell. If a player already controls a Field Spell, they can play a new one by sending the Field Spell from their Field Zone to the Graveyard by game mechanics (regardless of whether they activate or Set the new Field Spell).
Prior to 2014, the rules for Field Spell Cards were different. There could only be 1 face-up Field Spell on the field, between both players. If there was a face-up Field Spell in either player's Field Zone, while either player could play a new Field Spell, if they did any other face-up Field Spell in a Field Zone would be destroyed by game mechanics. Additionally, if a player had a Set card in their Field Zone and played a new Field Spell, the Set card would be destroyed by game mechanics. Because the card is destroyed by game mechanics, it is impossible to prevent, even with effects such as that of "Magical Citadel of Endymion".
Equip Cards continuously target the equipped monster. If that monster is no longer face-up on the field, the Equip Card is destroyed by game mechanics. Likewise, if the equipped monster is no longer an appropriate target for the Equip Card (e.g. if a monster equipped with Dragon Treasure is no longer Dragon-Type), the Equip Card is destroyed by game mechanics.
There are cards that, when combined together, create loops that can (and just might) never end. If an infinite loop with no net change is occurring, the card ruled to be the cause of the infinite loop is destroyed by game mechanics.