"which is artificial competition for entertainment, mental work is real productive work that benefits society"

Uhhh, professional sport isn't 'real' work? I would would say without a doubt every single processional athlete probably works much harder then your typical white collar worker (due to the fact that they are not typical athletes) As far as "productive" goes, each pro organization is staffed with hundreds of people all doing 'productive' work which is possible because of the athletes that work for the corporation.