The phrase "not wanting my kids to be dependent on me for their own happiness" pushed my buttons a little too, as I think of myself as very much responsible for my kids' happiness. But I see what MKKT is saying: it sounds like she's talking about the sense of entertaining kids to keep them from being bored. So I get that. I too did not engage in much play with my kids. I've never played tag, puppets, hide-and-seek, or Lego with them.
I am not a particularly boring mom, at least not according to my kids. I am a weird and embarrassing goofball some of the time -- playful, irreverent, self-deprecatingly silly, and so on -- but in ways that feel genuine to me and are part of who I am. I don't do those things in order to entertain them: I do them in order to entertain myself. If they are caught up in it, so much the better, but that's not my aim. And when they want to play, they do so without needing me as an appreciative audience, director or participant.
I hear what you're saying, pek64, about connecting meaningfully with kids through their play because it's something they genuinely want to do. But for us as unschoolers, when all learning and living is guided by the kids' autonomous choices, there's plenty of opportunity to connect meaningfully with my them -- because everything they do they have their own genuine reasons for wanting to do it. It's not like I spend all day making them do chores and schoolwork against their will, and then there's this small parcel of their lives that they enjoy, their play, in which I might connect with them in a positive way. I have plenty of chance to model maturity, to chat, to teach, to guide, while we're doing any of the myriad non-play things we do together for enjoyment and a sense of satisfaction throughout the day.