I don't know about others but I would consider that to be holding Goatee.
I shook my Ts hand when I first met her and we haven't touched since. She doesn't seem very touchy feely although I get a sense of being held by her presence sometimes. I don't think I would want to be touch to be part of our therapy though.
I am transitioning to a new t because my current T is leaving soon and I didn't shake the new ts hand when I met her. I don't know her well enough to guess if she is a touchy feely T or not. But I am pretty sure I wouldn't want touch from her either.