I find this analogy rather silly. Of course formal analogy can be drawn between aspects of the ancient games and modern sports, but what I find far more striking are the points of disanalogy: points which correspond instead to a culture that still retains some significant vestiges of having been Christianized. Yes, football stadiums remind us of the ancient coliseum, and all kinds of points of correspondence begin to crop up if you look for them: vendors, public latrines, crowd enthusiasm and taunting, etc.
But what was the striking feature of the Roman games? What is the feature that leaves us aghast? The gladiators fought to the death! They went out having pledged an oath to die in their grisly bloodsport. Furthermore, the vast majority of them were slaves, or those who had sold themselves into a slave class in desperation. In other words, they were some of them criminals, and in many cases innocents, forced to die for the pleasure of the crowd. This is precisely what we do not find in a sport like modern football. We have retained an enjoyment of physical prowess, teamwork, and competition, while at the same time we are taking pains to secure the safety and wellbeing of those who participate. Think about the amount of time, energy, and money that has gone in to designing just the helmet of a modern football player. When an actual injury is even suspected, play halts, and fans and players from both sides will look on in concern, often applauding in approval when the downed player walks off the field unharmed. And look at what football players are payed. We remunerate them in keeping with the enjoyment we get from watching them perform. In other words, in this (post)-Christian society, we have retained what was worthwhile for entertainment and leisure while excising the evil bloodlust and honoring those who impress us with their hard work and skill. This is as it should be.
Football is similar to the gladiatorial games in many ways, but they are superficial ways. They are nothing more than formal correspondences that you would expect. Any society will have public leisure events, competitions, gathering places where fans cheer for a team or an individual, etc. But in our case the differences, not the similarities, are where the profundity is to be found.