I had this card set face down as a trap and my opponent used a quick play spell when I attacked one of his monsters to cut my monsters attack in half and the anti magic prism didn't activate. I clicked on it and stuff to see if I had to activate it manually and nothing happened. Since It didn't activate, my opponent was able to tribute and monster from his 2 monsters on the field. His monsters effect was to clear any card on my board. So I had nothing to defend with and 1150 health, and of course, if the anti magic prism would have activated, all that would have never been able to happen cuz I would have destroyed his monster, dissableing him from doing a tribute summon.
the exact same thing happened to me, the card was half shut and i had my anti magic prism down from turn 1. I attack, he uses half shut and i expect to destroy his monster anyway and direct attack but no activation from AMP and costs me the game next turn. No idea what happened.
The quickplay in question sounds like it was activated in the damage step. Only certain cards can be activated in the damage step (such as counter trap cards, quick effects that negate, effects that change the attack/defense of a monster, and a few others). Anti-Magic Prism is not a Counter Trap card. The person probably activated the card in damage step to which you cant chain AMP