I was showing to my nephew (10) how to play chess recently. It wasn't until my sister came along and started to interact with him that I noticed the difference in her demeanor towards him compared to mine. For a second this nearly made me feel as if I should have more authority in such a situation, but it's actually fine not to. I think some people either perhaps don't empathise as much or else they think that they need to keep the kids at arms length in order for them to respect.
I'm obviously completely aware that there's certain things children wouldn't be aware of that us adults would be, and I would account for this in some sort of way when interacting with them... and would be able to be in charge when needed. But beyond that I wouldn't sense that I interact with them any differently. I'm not saying that people who don't talk to kids as equals are disrespectful, or they the kids are offended; just that there's a difference between some adults in this manner.