The entertainment and sports industry will never die on a world-wide basis. It may well be that certain segments of the industry will die worldwide or within a country. However, the whole industry will never die so long as there is mass media and the general public has some money.
We can see that there has been demand for entertainment for at least as long as there has been mass media. During the Great Depression in the United States, movies and sports were big business. People were willing to spend on entertainment as a way to escape their problems. If entertainment could continue to be strong in those circumstances, it is extremely unlikely that it will ever die off.
Of course, aspects of the industry could die off in any country. The horse racing industry in the US, for example, is doing very poorly and may not survive. However, the entertainment industry as a whole will survive.