He (Shakepeare) usually wrote for a specific group of actors and as they became older he wrote / was writing plays with other characters in mind.
It's part of an exercise from a textbook. I think wrote is correct. And you?
If I were a native speaker of English, I would never shut up. :-)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.