Can there exist a second Chess, in which all the pieces move in the same way as the first and yet is still distinct? I suppose it is possible that a group of people could have a club where they play "chess2", yet it would be very difficult for this club to legitimize itself among the global population.

This may seem a silly metaphor but actually both Chess and Bitcoin exist as a concept through social consensus; they are what we believe them to be. So yes, technically a "second Bitcoin" can appear. But it's rather doubtful it would be taken seriously. More likely would be /modified/ versions where the rules are slightly different. These can actually claim to exist as distinct and exist under new names, like "Bitcoin Cash", but I'd still not call this "a second Bitcoin" but rather something new that competes.