Genco was dying in hospital for nearly a year, so it's said in the novel. Perhaps, he was somewhere else. We don't see Clemenza either. Maybe, they were celebrating Christmas (In that script it is Christmas for unknown reason, not Vito's birthday) with their own families, and Tessio had none, so they invited him.
I only know why there must be Tessio: the meaning of the scene is that Michael finally killed almost half people present in that happy room, and Tessio was one of them.