Yeah I often redirect the conversation into being about the other person and it's barely noticed. Not going to lie, that's my favorite. It's so efficient.
I think I worked with another ENFJ (retrospect typing) and she was so good at Grasshopper, it was amazing. I'd ask her a personal question and she toss it back at me and then I'd answer and volley it back to her. I don't know how to describe it. For all intents and purposes, when we would talk it would be a very seamless conversations, but it was hard (at least I felt that way) almost like squeezing blood out of a turnip. No lack of topics, no uncomfortable silences, but something was difficult about it. I don't know, I may have been imagining things

. We wouldn't talk over each other, but we both were trying to get personal info out but very reluctant to give any up.
This leads me to think do you wonder if it would be difficult for ENFJs to be friends with each other? I'm used to being in a position in my friendships (with the exception of about three people), that I'm the one that gives advice, I'm the only that helps out. Sometimes I resent the fact that I can't be the one in need, or maybe that I don't allow myself to be in that position, I don't know. When I am, it's like a raw exposed nerve, I hate that feeling and I want things to get to how they were ASAP. Maybe two ENFJs would face this problem of wanting the other person to divulge, but not willing to reveal.
Back to the games, Mindreader happens with family and the closest friends because that tends to get a bit intense. When you start claiming to know what people's true feelings and motives are and/or turn into Hector Projector, you'd better be close enough to them that you can kiss and makeup afterwards.