What does 任一牌 mean in Chinese "Magic: The Gathering" cards?
The confusion you had is on 任一牌，however, is is actually 任一牌手，where 手 means the person that is doing something with 牌。This is a common use in Chinese and specifically for your case, 牌手 means player, namely the person who is playing the cards.
Therefore the verb following it would be 施放 instead of 手施放，which would eventually mean discharge.
There are other examples like

水手 means sailor
刽子手 means executioner
围棋圣手 means the person who is really good at GO
赛车手 means racer
骑手 means bike rider