In American football, a play is a particular strategy (either offensive or defensive) that is employed during a down of the game. Each team will have their own set of plays that are compiled into a playbook, and every member of the team is expected to have completely memorized the playbook, so they know exactly what they are supposed to do when a play is invoked.
The implication in your quote is that the player in question needs the plays "taped to his wrist" (that is, written down and attached to his body for easy reference) because he cannot be trusted to remember them. We'd need more context to know whether he is being called lazy (because he can't be bothered to study the playbook) or stupid (because he can't remember the plays even after studying).
The phrase "taped to his wrist" is not a common or well-known expression either in football or in English in general. It does, however, remind me of the common trope that a small child might be sent to school with a note pinned to their shirt from the parent to teacher, because small children cannot be trusted to convey important information or even to remember that they should be handing a note to their teacher.